Tootfinder

An Efficient Solution Method for Solving Convex Separable Quadratic Optimization Problems
Shaoze Li, Junhao Wu, Cheng Lu, Zhibin Deng, Shu-Cherng Fang
https://arxiv.org/abs/2510.11554

An Efficient Solution Method for Solving Convex Separable Quadratic Optimization Problems
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with a convex separable objective function subject to multiple convex separable constraints. We show that the proposed approach leads to a dual coordinate ascent algorithm and provide a convergence proof. Numerical experiments support the superior performance of …

Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization
James Usevitch, Juan Augusto Paredes Salazar, Ankit Goel
https://arxiv.org/abs/2510.09925

Computing Safe Control Inputs using Discrete-Time Matrix Control Barrier Functions via Convex Optimization
Control barrier functions (CBFs) have seen widespread success in providing forward invariance and safety guarantees for dynamical control systems. A crucial limitation of discrete-time formulations is that CBFs that are nonconcave in their argument require the solution of nonconvex optimization problems to compute safety-preserving control inputs, which inhibits real-time computation of control inputs guaranteeing forward invariance. This paper presents a novel method for computing safety-prese…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
Chuan He, Zhaosong Lu
https://arxiv.org/abs/2510.11676 https://a…

Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex function whose subgradients are estimated under heavy-tailed noise. Existing work often employs gradient clipping or normalization techniques in stochastic first-order methods to address heavy-tailed noise. In this paper, we demonstrate that a vanilla stochastic algorithm -- without additional modifications such as clipping or normalization -- can achieve op…

MATStruct: High-Quality Medial Mesh Computation via Structure-aware Variational Optimization
Ningna Wang, Rui Xu, Yibo Yin, Zichun Zhong, Taku Komura, Wenping Wang, Xiaohu Guo
https://arxiv.org/abs/2510.10751

MATStruct: High-Quality Medial Mesh Computation via Structure-aware Variational Optimization
We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and junctions, provides a natural volumetric decomposition of a 3D shape. Our method introduces a structure-aware, particle-based optimization pipeline guided by the restricted power diagram (RPD), which partitions the input volume into convex cells whose dual e…

A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization
Qing-xin Meng, Xia Lei, Jian-wei Liu
https://arxiv.org/abs/2509.07901 https://arx…

A Modular Algorithm for Non-Stationary Online Convex-Concave Optimization
This paper investigates the problem of Online Convex-Concave Optimization, which extends Online Convex Optimization to two-player time-varying convex-concave games. The goal is to minimize the dynamic duality gap (D-DGap), a critical performance measure that evaluates players' strategies against arbitrary comparator sequences. Existing algorithms fail to deliver optimal performance, particularly in stationary or predictable environments. To address this, we propose a novel modular algorithm wit…

Global Solutions to Non-Convex Functional Constrained Problems with Hidden Convexity
Ilyas Fatkhullin, Niao He, Guanghui Lan, Florian Wolf
https://arxiv.org/abs/2511.10626 https://arxiv.org/pdf/2511.10626 https://arxiv.org/html/2511.10626
arXiv:2511.10626v1 Announce Type: new
Abstract: Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and reinforcement learning, such problems possess hidden convexity, meaning they can be reformulated as convex programs via a nonlinear invertible transformation. Typically such transformations are implicit or unknown, making the direct link with the convex program impossible. On the other hand, (sub-)gradients with respect to the original variables are often accessible or can be easily estimated, which motivates algorithms that operate directly in the original (non-convex) problem space using standard (sub-)gradient oracles. In this work, we develop the first algorithms to provably solve such non-convex problems to global minima. First, using a modified inexact proximal point method, we establish global last-iterate convergence guarantees with $\widetilde{\mathcal{O}}(\varepsilon^{-3})$ oracle complexity in non-smooth setting. For smooth problems, we propose a new bundle-level type method based on linearly constrained quadratic subproblems, improving the oracle complexity to $\widetilde{\mathcal{O}}(\varepsilon^{-1})$. Surprisingly, despite non-convexity, our methodology does not require any constraint qualifications, can handle hidden convex equality constraints, and achieves complexities matching those for solving unconstrained hidden convex optimization.
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Verification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
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Neuro-inspired automated lens design
Yao Gao, Lei Sun, Shaohua Gao, Qi Jiang, Kailun Yang, Weijian Hu, Xiaolong Qian, Wenyong Li, Luc Van Gool, Kaiwei Wang
https://arxiv.org/abs/2510.09979

Neuro-inspired automated lens design
The highly non-convex optimization landscape of modern lens design necessitates extensive human expertise, resulting in inefficiency and constrained design diversity. While automated methods are desirable, existing approaches remain limited to simple tasks or produce complex lenses with suboptimal image quality. Drawing inspiration from the synaptic pruning mechanism in mammalian neural development, this study proposes OptiNeuro--a novel automated lens design framework that first generates dive…

Efficient Convex Optimization for Bosonic State Tomography
Shengyong Li, Yanjin Yue, Ying Hu, Rui-Yang Gong, Qianchuan Zhao, Zhihui Peng, Pengtao Song, Zeliang Xiang, Jing Zhang
https://arxiv.org/abs/2509.06305

Efficient Convex Optimization for Bosonic State Tomography
Quantum states encoded in electromagnetic fields, also known as bosonic states, have been widely applied in quantum sensing, quantum communication, and quantum error correction. Accurate characterization is therefore essential yet difficult when states cannot be reconstructed with sparse Pauli measurements. Tomography must work with dense measurement bases, high-dimensional Hilbert spaces, and often sample-based data. However, existing convex optimization-based techniques are not efficient enou…

Separable convex optimization over indegree polytopes
N\'ora A. Borsik, P\'eter Madarasi
https://arxiv.org/abs/2509.06182 https://arxiv.org/pdf/250…

Separable convex optimization over indegree polytopes
We study egalitarian (acyclic) orientations of undirected graphs under indegree-based objectives, such as minimizing the $φ$-sum of indegrees for a strictly convex function $φ$, decreasing minimization (dec-min), and increasing maximization (inc-max). In the non-acyclic setting of Frank and Murota (2022), a single orientation simultaneously optimizes these three objectives, however, restricting to acyclic orientations confines us to the corners of the indegree polytope, where these fairness o…

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
Cody Melcher, Afrooz Jalilzadeh, Erfan Yazdandoost Hamedani
https://arxiv.org/abs/2510.11990

Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions tailored specifically for SP problems as extensions of quadratic growth conditions in minimization. These conditions relax the traditional requirement of strong convexity-strong concavity, thereby encompassing a broader class of problems. We propose a generali…

Convergence analysis of inexact MBA method for constrained upper-$\mathcal{C}^2$ optimization problems
Ruyu Liu, Shaohua Pan
https://arxiv.org/abs/2511.09940 https://arxiv.org/pdf/2511.09940 https://arxiv.org/html/2511.09940
arXiv:2511.09940v1 Announce Type: new
Abstract: This paper concerns a class of constrained optimization problems in which, the objective and constraint functions are both upper-$\mathcal{C}^2$. For such nonconvex and nonsmooth optimization problems, we develop an inexact moving balls approximation (MBA) method by a workable inexactness criterion for the solving of subproblems. By leveraging a global error bound for the strongly convex program associated with parametric optimization problems, we establish the full convergence of the iterate sequence under the partial bounded multiplier property (BMP) and the Kurdyka-{\L}ojasiewicz (KL) property of the constructed potential function, and achieve the local convergence rate of the iterate and objective value sequences if the potential function satisfies the KL property of exponent $q\in[1/2,1)$. A verifiable condition is also provided to check whether the potential function satisfies the KL property of exponent $q\in[1/2,1)$ at the given critical point. To the best of our knowledge, this is the first implementable inexact MBA method with a full convergence certificate for the constrained nonconvex and nonsmooth optimization problem.
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Some Applications and Limitations of Convex Optimization Hierarchies for Discrete and Continuous Optimization Problems
Mrinalkanti Ghosh
https://arxiv.org/abs/2508.21327 https:/…

Some Applications and Limitations of Convex Optimization Hierarchies for Discrete and Continuous Optimization Problems
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction problems (CSPs) by linear programming (LP) relaxations: for every CSP, the approximation obtained by a basic LP relaxation, is no weaker than the approximation obtained using relaxations given by super-constant levels of the Sherali-Adams hierarchy on instances of…

A quantum analogue of convex optimization
Eunou Lee
https://arxiv.org/abs/2510.02151 https://arxiv.org/pdf/2510.02151…

A quantum analogue of convex optimization
Convex optimization is the powerhouse behind the theory and practice of optimization. We introduce a quantum analogue of unconstrained convex optimization: computing the minimum eigenvalue of a Schrödinger operator $h = -Δ+ V $ with convex potential $V:\mathbb R^n \rightarrow \mathbb R_{\ge 0}$ such that $V(x)\rightarrow\infty $ as $\|x\|\rightarrow\infty$. For this problem, we present an efficient quantum algorithm, called the Fundamental Gap Algorithm (FGA), that computes the mini…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
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Low-Rank Regularized Convex-Non-Convex Problems for Image Segmentation or Completion
Mohamed El Guide, Anas El Hachimi, Khalide Jbilou, Lothar Reichel
https://arxiv.org/abs/2508.21765

Low-Rank Regularized Convex-Non-Convex Problems for Image Segmentation or Completion
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one promotes low-rank structure in the solution, while the other one enforces smoothness. To solve the resulting optimization problem, we employ the alternating direction method of multipliers (ADMM). A detailed convergence analysis of the algorithm is provided, and th…

Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum
Reza Rahimi Baghbadorani, Sergio Grammatico, Peyman Mohajerin Esfahani
https://arxiv.org/abs/2511.10239 https://arxiv.org/pdf/2511.10239 https://arxiv.org/html/2511.10239
arXiv:2511.10239v1 Announce Type: new
Abstract: We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function is the sum of two nonsmooth functions. With regard to convergence rate, we provide the global (optimal) sublinear convergence guarantees of O(1/k), which is known to be provably optimal for the studied class of functions, along with a local linear rate if the nonsmooth term fulfills a so-call locally strong convexity condition. We validate the performance of our algorithm on several problem classes, including regression with the l1-norm (the Lasso problem), sparse semidefinite programming (the MaxCut problem), Nuclear norm minimization with application in model free fault diagnosis, and l_1-regularized model predictive control to showcase the benefits of the coupling. An interesting observation is that although our global convergence result guarantees O(1/k) convergence, we consistently observe a practical transient convergence rate of O(1/k^2), followed by asymptotic linear convergence as anticipated by the theoretical result. This two-phase behavior can also be explained in view of the proposed smoothing rule.
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Rate Maximization for UAV-assisted ISAC System with Fluid Antennas
Xingtao Yang, Zhenghe Guo, Siyun Liang, Zhaohui Yang, Chen Zhu, Zhaoyang Zhang
https://arxiv.org/abs/2510.07668

Rate Maximization for UAV-assisted ISAC System with Fluid Antennas
This letter investigates the joint sensing problem between unmanned aerial vehicles (UAV) and base stations (BS) in integrated sensing and communication (ISAC) systems with fluid antennas (FA). In this system, the BS enhances its sensing performance through the UAV's perception system. We aim to maximize the communication rate between the BS and UAV while guaranteeing the joint system's sensing capability. By establishing a communication-sensing model with convex optimization properties, we dec…

Post-disaster Max-Min Rate Optimization for Multi-UAV RSMA Network in Obstacle Environments
Qingyang Wang, Zhuohui Yao, Wenchi Cheng, Xiao Zheng
https://arxiv.org/abs/2509.23908

Post-disaster Max-Min Rate Optimization for Multi-UAV RSMA Network in Obstacle Environments
This paper proposes a rate-splitting multiple access (RSMA) transmission scheme to maximize the minimum achievable rate among ground users for emergency communications in post-disaster scenarios with obstacles, with which the optimal positioning of multiple unmanned aerial vehicle (UAV)-enabled base stations can be achieved timely.To address the resulting non-convex and intractable optimization problem, we design an alternating optimization approach. Specifically, we relax obstacle-related cons…

A Continuous Energy Ising Machine Leveraging Difference-of-Convex Programming
Debraj Banerjee, Santanu Mahapatra, Kunal Narayan Chaudhury
https://arxiv.org/abs/2509.01928 https:…

A Continuous Energy Ising Machine Leveraging Difference-of-Convex Programming
Many combinatorial optimization problems can be reformulated as the task of finding the ground state of a physical system, such as the Ising model. Most existing Ising solvers are inspired by simulated annealing. Although annealing techniques offer scalability, they lack convergence guarantees and are sensitive to the cooling schedule. We propose to solve the Ising problem by relaxing the binary spins to continuous variables and introducing a potential function (attractor) that steers the solut…

CoNeT-GIANT: A compressed Newton-type fully distributed optimization algorithm
Souvik Das, Subhrakanti Dey
https://arxiv.org/abs/2510.08806 https://arxiv.o…

CoNeT-GIANT: A compressed Newton-type fully distributed optimization algorithm
Compression techniques are essential in distributed optimization and learning algorithms with high-dimensional model parameters, particularly in scenarios with tight communication constraints such as limited bandwidth. This article presents a communication-efficient second-order distributed optimization algorithm, termed as CoNet-GIANT, equipped with a compression module, designed to minimize the average of local strongly convex functions. CoNet-GIANT incorporates two consensus-based averaging …

Self-concordant Schr\"odinger operators: spectral gaps and optimization without condition numbers
Sander Gribling, Simon Apers, Harold Nieuwboer, Michael Walter
https://arxiv.org/abs/2510.06115

Self-concordant Schrödinger operators: spectral gaps and optimization without condition numbers
Spectral gaps play a fundamental role in many areas of mathematics, computer science, and physics. In quantum mechanics, the spectral gap of Schrödinger operators has a long history of study due to its physical relevance, while in quantum computing spectral gaps are an important proxy for efficiency, such as in the quantum adiabatic algorithm. Motivated by convex optimization, we study Schrödinger operators associated with self-concordant barriers over convex domains and prove non-asymptotic …

On the Estimation of Multinomial Logit and Nested Logit Models: A Conic Optimization Approach
Hoang Giang Pham, Tien Mai, Minh Ha Hoang
https://arxiv.org/abs/2509.01562 https://…

On the Estimation of Multinomial Logit and Nested Logit Models: A Conic Optimization Approach
In this paper, we revisit parameter estimation for multinomial logit (MNL), nested logit (NL), and tree-nested logit (TNL) models through the framework of convex conic optimization. Traditional approaches typically solve the maximum likelihood estimation (MLE) problem using gradient-based methods, which are sensitive to step-size selection and initialization, and may therefore suffer from slow or unstable convergence. In contrast, we propose a novel estimation strategy that reformulates these m…

Integral Online Algorithms for Set Cover and Load Balancing with Convex Objectives
Thomas Kesselheim, Marco Molinaro, Kalen Patton, Sahil Singla
https://arxiv.org/abs/2508.18383

Integral Online Algorithms for Set Cover and Load Balancing with Convex Objectives
Online Set Cover and Load Balancing are central problems in online optimization, and there is a long line of work on developing algorithms for these problems with convex objectives. Although we know optimal online algorithms with $\ell_p$-norm objectives, recent developments for general norms and convex objectives that rely on the online primal-dual framework apply only to fractional settings due to large integrality gaps. Our work focuses on directly designing integral online algorithms for …

Memory Optimization for Convex Hull Support Point Queries
Michael Greer
https://arxiv.org/abs/2509.03753 https://arxiv.org/pdf/2509.03753

Memory Optimization for Convex Hull Support Point Queries
This paper evaluates several improvements to the memory layout of convex hulls to improve computation times for support point queries. The support point query is a fundamental part of common collision algorithms, and the work presented achieves a significant speedup depending on the number of vertices of the convex hull.

Neural Optimal Transport Meets Multivariate Conformal Prediction
Vladimir Kondratyev, Alexander Fishkov, Nikita Kotelevskii, Mahmoud Hegazy, Remi Flamary, Maxim Panov, Eric Moulines
https://arxiv.org/abs/2509.25444

Neural Optimal Transport Meets Multivariate Conformal Prediction
We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network…

Measuring dissimilarity between convex cones by means of max-min angles
Welington de Oliveira, Valentina Sessa, David Sossa
https://arxiv.org/abs/2511.10483 https://arxiv.org/pdf/2511.10483 https://arxiv.org/html/2511.10483
arXiv:2511.10483v1 Announce Type: new
Abstract: This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu-Hausdorff distance, a well-established metric for comparing compact sets. Furthermore, we examine cone configurations where the measure admits simplified or analytic forms. For the specific case of polyhedral cones, a nonconvex cutting-plane method is deployed to compute, at least approximately, the measure between them. Our approach builds on a tailored version of Kelley's cutting-plane algorithm, which involves solving a challenging master program per iteration. When this master program is solved locally, our method yields an angle that satisfies certain necessary optimality conditions of the underlying nonconvex optimization problem yielding the dissimilarity measure between the cones. As an application of the proposed mathematical and algorithmic framework, we address the image-set classification task under limited data conditions, a task that falls within the scope of the \emph{Few-Shot Learning} paradigm. In this context, image sets belonging to the same class are modeled as polyhedral cones, and our dissimilarity measure proves useful for understanding whether two image sets belong to the same class.
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dHPR: A Distributed Halpern Peaceman--Rachford Method for Non-smooth Distributed Optimization Problems
Zhangcheng Feng, Defeng Sun, Yancheng Yuan, Guojun Zhang
https://arxiv.org/abs/2511.10069 https://arxiv.org/pdf/2511.10069 https://arxiv.org/html/2511.10069
arXiv:2511.10069v1 Announce Type: new
Abstract: This paper introduces the distributed Halpern Peaceman--Rachford (dHPR) method, an efficient algorithm for solving distributed convex composite optimization problems with non-smooth objectives, which achieves a non-ergodic $O(1/k)$ iteration complexity regarding Karush--Kuhn--Tucker residual. By leveraging the symmetric Gauss--Seidel decomposition, the dHPR effectively decouples the linear operators in the objective functions and consensus constraints while maintaining parallelizability and avoiding additional large proximal terms, leading to a decentralized implementation with provably fast convergence. The superior performance of dHPR is demonstrated through comprehensive numerical experiments on distributed LASSO, group LASSO, and $L_1$-regularized logistic regression problems.
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Bridging the Prediction Error Method and Subspace Identification: A Weighted Null Space Fitting Method
Jiabao He, S. Joe Qin, H\r{a}kan Hjalmarsson
https://arxiv.org/abs/2510.02529

Bridging the Prediction Error Method and Subspace Identification: A Weighted Null Space Fitting Method
Subspace identification methods (SIMs) have proven to be very useful and numerically robust for building state-space models. While most SIMs are consistent, few if any can achieve the efficiency of the maximum likelihood estimate (MLE). Conversely, the prediction error method (PEM) with a quadratic criteria is equivalent to MLE, but it comes with non-convex optimization problems and requires good initialization points. This contribution proposes a weighted null space fitting (WNSF) approach for…

On the Strength of Linear Relaxations in Ordered Optimization
V\'ictor Blanco, Diego Laborda, Miguel Mart\'inez-Ant\'on
https://arxiv.org/abs/2510.09166 https://

On the Strength of Linear Relaxations in Ordered Optimization
We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity t…

Global Optimization via Softmin Energy Minimization
Andrea Agazzi, Vittorio Carlei, Marco Romito, Samuele Saviozzi
https://arxiv.org/abs/2509.17815 https://

Global Optimization via Softmin Energy Minimization
Global optimization, particularly for non-convex functions with multiple local minima, poses significant challenges for traditional gradient-based methods. While metaheuristic approaches offer empirical effectiveness, they often lack theoretical convergence guarantees and may disregard available gradient information. This paper introduces a novel gradient-based swarm particle optimization method designed to efficiently escape local minima and locate global optima. Our approach leverages a "Soft…

General formulation of an analytic, Lipschitz continuous control allocation for thrust-vectored controlled rigid-bodies
Frank Mukwege, Tam Willy Nguyen, Emanuele Garone
https://arxiv.org/abs/2510.08119

General formulation of an analytic, Lipschitz continuous control allocation for thrust-vectored controlled rigid-bodies
This study introduces a systematic and scalable method for arbitrary rigid-bodies equipped with vectorized thrusters. Two novel solutions are proposed: a closed-form, Lipschitz continuous mapping that ensures smooth actuator orientation references, and a convex optimization formulation capable of handling practical actuator constraints such as thrust saturation and angular rate limits. Both methods leverage the null-space structure of the allocation mapping to perform singularity avoidance whil…

Crosslisted article(s) found for cs.CG. https://arxiv.org/list/cs.CG/new
[1/1]:
- Memory Optimization for Convex Hull Support Point Queries
Michael Greer
https://…

Pinching Antenna Systems (PASS) for Cell-Free Communications
Haochen Li
https://arxiv.org/abs/2510.03628 https://arxiv.org/pdf/2510.03628

Pinching Antenna Systems (PASS) for Cell-Free Communications
A pinching antenna system (PASS) assisted cell-free communication system is proposed. A sum rate maximization problem under the BS power budget constraint and PA deployment constraint is formulated. To tackle the proposed non-convex optimization problem, an alternating optimization (AO) algorithm is developed. In particular, the digital beamforming sub-problem is solved using the weighted minimum mean square error (WMMSE) method, whereas the pinching beamforming sub-problem is handled via a pen…

Quantum Alternating Direction Method of Multipliers for Semidefinite Programming
Hantao Nie, Dong An, Zaiwen Wen
https://arxiv.org/abs/2510.10056 https://a…

Quantum Alternating Direction Method of Multipliers for Semidefinite Programming
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and performing eigenvalue decompositions. In this paper, we present a quantum alternating direction method of multipliers (QADMM) for SDPs, building on recent advances in quantum computing. An inexact ADMM framework is developed, which tolerates errors in the iterates …

Heuristic Bundle Upper Bound Based Polyhedral Bundle Method for Semidefinite Programming
Zilong Cui, Ran Gu
https://arxiv.org/abs/2510.12374 https://arxiv.…

Heuristic Bundle Upper Bound Based Polyhedral Bundle Method for Semidefinite Programming
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the polyhedral bundle method to standard SDPs. The basic idea of this method is to approximate semidefinite constraints using linear constraints, and thereby transform the SDP problem into a series of quadratic programming subproblems. However, the number of linear constr…

An Inexact Proximal Framework for Nonsmooth Riemannian Difference-of-Convex Optimization
Bo Jiang, Meng Xu, Xingju Cai, Ya-Feng Liu
https://arxiv.org/abs/2509.08561 https://

An Inexact Proximal Framework for Nonsmooth Riemannian Difference-of-Convex Optimization
Nonsmooth Riemannian optimization has attracted increasing attention, especially in problems with sparse structures. While existing formulations typically involve convex nonsmooth terms, incorporating nonsmooth difference-of-convex (DC) penalties can enhance recovery accuracy. In this paper, we study a class of nonsmooth Riemannian optimization problems whose objective is the sum of a smooth function and a nonsmooth DC term. We establish, for the first time in the manifold setting, the equivale…

Convexity of Optimization Curves: Local Sharp Thresholds, Robustness Impossibility, and New Counterexamples
Le Duc Hieu
https://arxiv.org/abs/2509.08954 https://

Convexity of Optimization Curves: Local Sharp Thresholds, Robustness Impossibility, and New Counterexamples
We study when the \emph{optimization curve} of first--order methods -- the sequence \${f(x\_n)}*{n\ge0}\$ produced by constant--stepsize iterations -- is convex, equivalently when the forward differences \$f(x\_n)-f(x*{n+1})\$ are nonincreasing. For gradient descent (GD) on convex \$L\$--smooth functions, the curve is convex for all stepsizes \$η\le 1.75/L\$, and this threshold is tight. Moreover, gradient norms are nonincreasing for all \$η\le 2/L\$, and in continuous time (gradient flow) th…

A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation
Kelin Wu, Hongpeng Sun
https://arxiv.org/abs/2509.09391 …

A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation
This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit parts and a third-order backward differentiation formula for the implicit part of the gradient flow in variational functions. The proposed algorithm, akin to a generalized difference-of-convex (DC) approach, employs a changing set of convex functions in each…

On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
Arnab Auddy, Ming Yuan
https://arxiv.org/abs/2509.25126 https://arxiv.…

On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms
We study spectral learning for orthogonally decomposable (odeco) tensors, emphasizing the interplay between statistical limits, optimization geometry, and initialization. Unlike matrices, recovery for odeco tensors does not hinge on eigengaps, yielding improved robustness under noise. While iterative methods such as tensor power iterations can be statistically efficient, initialization emerges as the main computational bottleneck. We investigate perturbation bounds, non-convex optimization anal…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- A robust BFGS algorithm for unconstrained nonlinear optimization problems
Yaguang Yang
https://arxiv.org/abs/1212.5929
- Quantum computing and the stable set problem
Alja\v{z} Krpan, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2405.12845 https://mastoxiv.page/@arXiv_mathOC_bot/112483516437815686
- Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach
Zongxia Liang, Xiang Yu, Keyu Zhang
https://arxiv.org/abs/2508.20388 https://mastoxiv.page/@arXiv_mathOC_bot/115111048711698998
- Differential Dynamic Programming for the Optimal Control Problem with an Ellipsoidal Target Set a...
Sungjun Eom, Gyunghoon Park
https://arxiv.org/abs/2509.07546 https://mastoxiv.page/@arXiv_mathOC_bot/115179281556444440
- On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
https://arxiv.org/abs/2509.13960 https://mastoxiv.page/@arXiv_mathOC_bot/115224514482363803
- Automated algorithm design via Nevanlinna-Pick interpolation
Ibrahim K. Ozaslan, Tryphon T. Georgiou, Mihailo R. Jovanovic
https://arxiv.org/abs/2509.21416 https://mastoxiv.page/@arXiv_mathOC_bot/115286533597711930
- Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment
Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11381 https://mastoxiv.page/@arXiv_mathOC_bot/115372322896073250
- Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Co...
Yingdong Yin
https://arxiv.org/abs/2510.26382 https://mastoxiv.page/@arXiv_mathOC_bot/115468018035252078
- History-Aware Adaptive High-Order Tensor Regularization
Chang He, Bo Jiang, Yuntian Jiang, Chuwen Zhang, Shuzhong Zhang
https://arxiv.org/abs/2511.05788
- Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems
Jos\'e Antonio Carrillo, Sondre Tesdal Galtung
https://arxiv.org/abs/2312.04932 https://mastoxiv.page/@arXiv_mathAP_bot/111560077272113052
- Kernel Modelling of Fading Memory Systems
Yongkang Huo, Thomas Chaffey, Rodolphe Sepulchre
https://arxiv.org/abs/2403.11945 https://mastoxiv.page/@arXiv_eessSY_bot/112121123836064435
- The Maximum Theoretical Ground Speed of the Wheeled Vehicle
Altay Zhakatayev, Mukatai Nemerebayev
https://arxiv.org/abs/2502.15341 https://mastoxiv.page/@arXiv_physicsclassph_bot/114057765769441123
- Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
Giacomo Greco, Luca Tamanini
https://arxiv.org/abs/2504.11133 https://mastoxiv.page/@arXiv_mathPR_bot/114346453424694503
- Optimizing the ground state energy of the three-dimensional magnetic Dirichlet Laplacian with con...
Matthias Baur
https://arxiv.org/abs/2504.21597 https://mastoxiv.page/@arXiv_mathph_bot/114431404740241516
- A localized consensus-based sampling algorithm
Arne Bouillon, Alexander Bodard, Panagiotis Patrinos, Dirk Nuyens, Giovanni Samaey
https://arxiv.org/abs/2505.24861 https://mastoxiv.page/@arXiv_mathNA_bot/114612580684567066
- A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
https://arxiv.org/abs/2508.02364 https://mastoxiv.page/@arXiv_csLG_bot/114976243138728278
- Minimal Regret Walras Equilibria for Combinatorial Markets via Duality, Integrality, and Sensitiv...
Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz
https://arxiv.org/abs/2511.09021 https://mastoxiv.page/@arXiv_csGT_bot/115541243299714775
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User Manual for Model-based Imaging Inverse Problem
Xiaodong Wang
https://arxiv.org/abs/2509.01572 https://arxiv.org/pdf/2509.01572

User Manual for Model-based Imaging Inverse Problem
This user manual is intended to provide a detailed description on model-based optimization for imaging inverse problem. Theseproblems can be particularly complex and challenging, especially for individuals without prior exposure to convex optimization orinverse problem theory, like myself. In light of this, I am writing this manual to clarify and systematically organize the mathematicalrationale underlying imaging inverse problems. This manual might not be accurate in mathmatical notion but mor…

GaussianPSL: A novel framework based on Gaussian Splatting for exploring the Pareto frontier in multi-criteria optimization
Phuong Mai Dinh, Van-Nam Huynh
https://arxiv.org/abs/2509.17889

GaussianPSL: A novel framework based on Gaussian Splatting for exploring the Pareto frontier in multi-criteria optimization
Multi-objective optimization (MOO) is essential for solving complex real-world problems involving multiple conflicting objectives. However, many practical applications - including engineering design, autonomous systems, and machine learning - often yield non-convex, degenerate, or discontinuous Pareto frontiers, which involve traditional scalarization and Pareto Set Learning (PSL) methods that struggle to approximate accurately. Existing PSL approaches perform well on convex fronts but tend to …

A Duality Theorem for Classical-Quantum States with Applications to Complete Relational Program Logics
Gilles Barthe, Minbo Gao, Jam Kabeer Ali Khan, Matthijs Muis, Ivan Renison, Keiya Sakabe, Michael Walter, Yingte Xu, Li Zhou
https://arxiv.org/abs/2510.07051

A Duality Theorem for Classical-Quantum States with Applications to Complete Relational Program Logics
Duality theorems play a fundamental role in convex optimization. Recently, it was shown how duality theorems for countable probability distributions and finite-dimensional quantum states can be leveraged for building relatively complete relational program logics for probabilistic and quantum programs, respectively. However, complete relational logics for classical-quantum programs, which combine classical and quantum computations and operate over classical as well as quantum variables, have rem…

Communication over LQG Control Systems: A Convex Optimization Approach to Capacity
Aharon Rips, Oron Sabag
https://arxiv.org/abs/2509.17002 https://arxiv.o…

Communication over LQG Control Systems: A Convex Optimization Approach to Capacity
We study communication over control systems, where a controller-encoder selects inputs to a dynamical system in order to simultaneously regulate the system and convey a message to an observer that has access to the system's output measurements. This setup reflects implicit communication, as the controller embeds a message in the control signal. The capacity of a control system is the maximal reliable rate of the embedded message subject to a closed-loop control-cost constraint. We focus on line…

First-order SDSOS-convex semi-algebraic optimization and exact SOCP relaxations
Chengmiao Yang, Liguo Jiao, Jae Hyoung Lee
https://arxiv.org/abs/2509.07418 https://

First-order SDSOS-convex semi-algebraic optimization and exact SOCP relaxations
In this paper, we define a new type of nonsmooth convex function, called {\em first-order SDSOS-convex semi-algebraic function}, which is an extension of the previously proposed first-order SDSOS-convex polynomials (Chuong et al. in J Global Optim 75:885--919, 2019). This class of nonsmooth convex functions contains many well-known functions, such as the Euclidean norm, the $\ell_1$-norm commonly used in compressed sensing and sparse optimization, and the least squares function frequently emplo…

Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective
Xu Shang, Yang Zheng
https://arxiv.org/abs/2509.09027 https://arxiv.org/p…

Regularization in Data-driven Predictive Control: A Convex Relaxation Perspective
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive control as an outer problem. Within this framework, we show that several regularized DDPC formulations, including l1-norm penalties, projection-based regularizers, and a newly introduced causality-based regularizer, can be viewed as convex relaxations of their resp…

Inertial accelerated primal-dual algorithms for non-smooth convex optimization problems with linear equality constraints
Huan Zhang, Xiangkai Sun, Shengjie Li, Kok Lay Teo
https://arxiv.org/abs/2509.07306

Inertial accelerated primal-dual algorithms for non-smooth convex optimization problems with linear equality constraints
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality constraints. We first introduce a second-order differential system with time scaling associated with the non-smooth convex optimization problem, and then obtain fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along…

Hidden Convexity in Active Learning: A Convexified Online Input Design for ARX Systems
Nicolas Chatzikiriakos, Bowen Song, Philipp Rank, Andrea Iannelli
https://arxiv.org/abs/2509.03257

Hidden Convexity in Active Learning: A Convexified Online Input Design for ARX Systems
The goal of this work is to accelerate the identification of an unknown ARX system from trajectory data through online input design. Specifically, we present an active learning algorithm that sequentially selects the input to excite the system according to an experiment design criterion using the past measured data. The adopted criterion yields a non-convex optimization problem, but we provide an exact convex reformulation allowing to find the global optimizer in a computationally tractable way…

Re$^3$MCN: Cubic Newton Variance Reduction Momentum Quadratic Regularization for Finite-sum Non-convex Problems
Dmitry Pasechnyuk-Vilensky, Dmitry Kamzolov, Martin Tak\'a\v{c}
https://arxiv.org/abs/2510.08714

Re$^3$MCN: Cubic Newton + Variance Reduction + Momentum + Quadratic Regularization for Finite-sum Non-convex Problems
We analyze a stochastic cubic regularized Newton method for finite sum optimization $\textstyle\min_{x\in\mathbb{R}^d} F(x) \;=\; \frac{1}{n}\sum_{i=1}^n f_i(x)$, that uses SARAH-type recursive variance reduction with mini-batches of size $b\sim n^{1/2}$ and exponential moving averages (EMA) for gradient and Hessian estimators. We show that the method achieves a $(\varepsilon,\sqrt{L_2\varepsilon})$-second-order stationary point (SOSP) with total stochastic oracle calls $n + \widetilde{\mathcal…

Fast Convergence Rates for Subsampled Natural Gradient Algorithms on Quadratic Model Problems
Gil Goldshlager, Jiang Hu, Lin Lin
https://arxiv.org/abs/2508.21022 https://…

Fast Convergence Rates for Subsampled Natural Gradient Algorithms on Quadratic Model Problems
Subsampled natural gradient descent (SNGD) has shown impressive results for parametric optimization tasks in scientific machine learning, such as neural network wavefunctions and physics-informed neural networks, but it has lacked a theoretical explanation. We address this gap by analyzing the convergence of SNGD and its accelerated variant, SPRING, for idealized parametric optimization problems where the model is linear and the loss function is strongly convex and quadratic. In the special cas…

Halpern Acceleration of the Inexact Proximal Point Method of Rockafellar
Liwei Zhang, Fanli Zhuang, Ning Zhang
https://arxiv.org/abs/2511.10372 https://arxiv.org/pdf/2511.10372 https://arxiv.org/html/2511.10372
arXiv:2511.10372v1 Announce Type: new
Abstract: This paper investigates a Halpern acceleration of the inexact proximal point method for solving maximal monotone inclusion problems in Hilbert spaces. The proposed Halpern inexact proximal point method (HiPPM) is shown to be globally convergent, and a unified framework is developed to analyze its worst-case convergence rate. Under mild summability conditions on the inexactness tolerances, HiPPM achieves an $\mathcal{O}(1/k^{2})$ rate in terms of the squared fixed-point residual. Furthermore, under additional mild condition, the method retains a fast linear convergence rate. Building upon this framework, we further extend the acceleration technique to constrained convex optimization through the augmented Lagrangian formulation. In analogy to Rockafellar's classical results, the resulting accelerated inexact augmented Lagrangian method inherits the convergence rate and complexity guarantees of HiPPM. The analysis thus provides a unified theoretical foundation for accelerated inexact proximal algorithms and their augmented Lagrangian extensions.
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Sharpness of Minima in Deep Matrix Factorization: Exact Expressions
Anil Kamber, Rahul Parhi
https://arxiv.org/abs/2509.25783 https://arxiv.org/pdf/2509.25…

Sharpness of Minima in Deep Matrix Factorization: Exact Expressions
Understanding the geometry of the loss landscape near a minimum is key to explaining the implicit bias of gradient-based methods in non-convex optimization problems such as deep neural network training and deep matrix factorization. A central quantity to characterize this geometry is the maximum eigenvalue of the Hessian of the loss, which measures the sharpness of the landscape. Currently, its precise role has been obfuscated because no exact expressions for this sharpness measure were known i…

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
Xin He, Ya-Ping Fang
https://arxiv.org/abs/2509.08258

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $μ_F$- and $μ_G$-strongly convex functions, respectively. By incorporating Nesterov acceleration for strongly convex optimization, we first propose an optimal first-order discrete primal-dual gradient algorithm. We show that it achieves the optimal convergence rate $\mathcal{O}\left(\left(1 - \min\left\{\sqrt{\frac{μ_F}{L_F}}, \sqrt{\frac{μ_G}{L_G…

Convergence for adaptive resampling of random Fourier features
Xin Huang, Aku Kammonen, Anamika Pandey, Mattias Sandberg, Erik von Schwerin, Anders Szepessy, Ra\'ul Tempone
https://arxiv.org/abs/2509.03151

Convergence for adaptive resampling of random Fourier features
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier frequencies. The challenge is to sample the Fourier frequencies well. This work proves convergence of a data adaptive method based on resampling the frequencies asymptotically optimally, as the number of nodes and amount of data tend to infinity. Numerical resul…

Universal Representation of Generalized Convex Functions and their Gradients
Moeen Nehzati
https://arxiv.org/abs/2509.04477 https://arxiv.org/pdf/2509.0447…

Universal Representation of Generalized Convex Functions and their Gradients
Solutions to a wide range of optimization problems, from optimal transport theory to mathematical economics, often take the form of generalized convex functions (GCFs). This characterization can be used to convert nested bilevel optimization problems into single-level optimization problems. Despite this, the characterization has not been fully exploited in numerical optimization. When the solution to an optimization problem is known to belong to a particular class of objects, this information…

A Monte Carlo Approach to Nonsmooth Convex Optimization via Proximal Splitting Algorithms
Nicholas Di, Eric C. Chi, Samy Wu Fung
https://arxiv.org/abs/2509.07914 https://…

A Monte Carlo Approach to Nonsmooth Convex Optimization via Proximal Splitting Algorithms
Operator splitting algorithms are a cornerstone of modern first-order optimization, relying critically on proximal operators as their fundamental building blocks. However, explicit formulas for proximal operators are available only for limited classes of functions, restricting the applicability of these methods. Recent work introduced HJ-Prox, a zeroth-order Monte Carlo approximation of the proximal operator derived from Hamilton-Jacobi PDEs, which circumvents the need for closed-form solutions…

Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
Emre Sahinoglu, Shahin Shahrampour
https://arxiv.org/abs/2509.07779 https://arxiv.or…

Decentralized Online Riemannian Optimization Beyond Hadamard Manifolds
We study decentralized online Riemannian optimization over manifolds with possibly positive curvature, going beyond the Hadamard manifold setting. Decentralized optimization techniques rely on a consensus step that is well understood in Euclidean spaces because of their linearity. However, in positively curved Riemannian spaces, a main technical challenge is that geodesic distances may not induce a globally convex structure. In this work, we first analyze a curvature-aware Riemannian consensus …

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Damped Proximal Augmented Lagrangian Method for weakly-Convex Problems with Convex Constraints
Hari Dahal, Wei Liu, Yangyang Xu

Smooth Quasar-Convex Optimization with Constraints
David Mart\'inez-Rubio
https://arxiv.org/abs/2510.01943 https://arxiv.org/pdf/2510.01943

Smooth Quasar-Convex Optimization with Constraints
Quasar-convex functions form a broad nonconvex class with applications to linear dynamical systems, generalized linear models, and Riemannian optimization, among others. Current nearly optimal algorithms work only in affine spaces due to the loss of one degree of freedom when working with general convex constraints. Obtaining an accelerated algorithm that makes nearly optimal $\widetilde{O}(1/(γ\sqrtε))$ first-order queries to a $γ$-quasar convex smooth function \emph{with constraints} was i…

Long-Time Analysis of Stochastic Heavy Ball Dynamics for Convex Optimization and Monotone Equations
Radu Ioan Bot, Chiara Schindler
https://arxiv.org/abs/2510.02951 https://

Long-Time Analysis of Stochastic Heavy Ball Dynamics for Convex Optimization and Monotone Equations
In a separable real Hilbert space, we study the problem of minimizing a convex function with Lipschitz continuous gradient in the presence of noisy evaluations. To this end, we associate a stochastic Heavy Ball system, incorporating a friction coefficient, with the optimization problem. We establish existence and uniqueness of trajectory solutions for this system. Under a square integrability condition for the diffusion term, we prove almost sure convergence of the trajectory process to an opti…

A Proximal Descent Method for Minimizing Weakly Convex Optimization
Feng-Yi Liao, Yang Zheng
https://arxiv.org/abs/2509.02804 https://arxiv.org/pdf/2509.02…

A Proximal Descent Method for Minimizing Weakly Convex Optimization
We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a $\textit{proximal descent method}$, a simple and efficient first-order algorithm that combines the inexact proximal point method with classical convex bundle techniques. Our analysis establishes explicit non-asymptotic convergence rates in terms of $(η,ε)$-inexact stati…

The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization
Kevin Tracy, John Z. Zhang, Jon Arrizabalaga, Stefan Schaal, Yuval Tassa, Tom Erez, Zachary Manchester
https://arxiv.org/abs/2509.26575

The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization
We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a der…

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Jeremy Bertoncini, Alberto De Marchi, Matthias Gerdts, Simon Gottschalk
https://arxiv.org/abs/2509.07404

Reinforcement learning for online hyperparameter tuning in convex quadratic programming
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow tail-convergence typical of first-order schemes, thus requiring many iterations to achieve high-accuracy solutions. Moreover, hyperparameter tuning significantly impacts on the solver performance but how to find an appropriate parameter configuration remains an elusive …

Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions
Endrit Dosti, Sergiy A. Vorobyov, Themistoklis Charalambous
https://arxiv.org/abs/2510.02965

Estimating Sequences with Memory for Minimizing Convex Non-smooth Composite Functions
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce a new class of generalized composite estimating sequences, devised by exploiting the information embedded in the iterates generated during the minimization process. Building on these sequences, we propose a novel accelerated first-order method tailored for su…

Convex Pollution Control of Wastewater Treatment Systems
Joshua Taylor
https://arxiv.org/abs/2510.03918 https://arxiv.org/pdf/2510.03918

Convex Pollution Control of Wastewater Treatment Systems
We design a model-predictive controller for managing the actuators in sewer networks. It minimizes flooding and combined-sewer overflow during rain and pollution at other times. To make the problem tractable, we use a convex relaxation of the microbial growth kinetics and a physically motivated linearization of the mass flow bilinearities. With these approximations, the trajectory optimization in each control period is a second-order cone program. In simulation, the controller releases roughly …

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
Nazar Emirov, Guohui Song, Qiyu Sun
https://arxiv.org/abs/2510.01511

Exponential convergence of a distributed divide-and-conquer algorithm for constrained convex optimization on networks
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration solves local subproblems around selected fusion centers and coordinates only with neighboring fusion centers. Under standard assumptions of smoothness, strong convexity, and locality on the objective function, together with polynomial growth conditions on the …

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
Xiaokai Chang, Junfeng Yang, Jianchao Bai, Jianxiong Cao
https://arxiv.org/abs/2510.00437

A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
The primal-dual splitting algorithm (PDSA) by Chambolle and Pock is efficient for solving structured convex optimization problems. It adopts an extrapolation step and achieves convergence under certain step size condition. Chang and Yang recently proposed a modified PDSA for bilinear saddle point problems, integrating a convex combination step to enable convergence with extended step sizes. In this paper, we focus on composite monotone inclusion problems (CMIPs), a generalization of convex opti…

ProxSTORM -- A Stochastic Trust-Region Algorithm for Nonsmooth Optimization
Robert J. Baraldi, Aurya Javeed, Drew P. Kouri, Katya Scheinberg
https://arxiv.org/abs/2510.03187 htt…

ProxSTORM -- A Stochastic Trust-Region Algorithm for Nonsmooth Optimization
We develop a stochastic trust-region algorithm for minimizing the sum of a possibly nonconvex Lipschitz-smooth function that can only be evaluated stochastically and a nonsmooth, deterministic, convex function. This algorithm, which we call ProxSTORM, generalizes STORM [1, 2] -- a stochastic trust-region algorithm for the unconstrained optimization of smooth functions -- and the inexact deterministic proximal trust-region algorithm in [3]. We generalize and, in some cases, simplify problem assu…

Convergence, Duality and Well-Posedness in Convex Bilevel Optimization
Khanh-Hung Giang-Tran, Nam Ho-Nguyen, Fatma K{\i}l{\i}n\c{c}-Karzan, Lingqing Shen
https://arxiv.org/abs/2509.18304

Simplex Frank-Wolfe: Linear Convergence and Its Numerical Efficiency for Convex Optimization over Polytopes
Haoning Wang, Houduo Qi, Liping Zhang
https://arxiv.org/abs/2509.24279

Simplex Frank-Wolfe: Linear Convergence and Its Numerical Efficiency for Convex Optimization over Polytopes
We investigate variants of the Frank-Wolfe (FW) algorithm for smoothing and strongly convex optimization over polyhedral sets, with the goal of designing algorithms that achieve linear convergence while minimizing per-iteration complexity as much as possible. Starting from the simple yet fundamental unit simplex, and based on geometrically intuitive motivations, we introduce a novel oracle called Simplex Linear Minimization Oracle (SLMO), which can be implemented with the same complexity as the…

Faster Gradient Methods for Highly-smooth Stochastic Bilevel Optimization
Lesi Chen, Junru Li, Jingzhao Zhang
https://arxiv.org/abs/2509.02937 https://arxi…

Faster Gradient Methods for Highly-smooth Stochastic Bilevel Optimization
This paper studies the complexity of finding an $ε$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order method, F${}^2$SA, achieving the $\tilde{\mathcal{O}}(ε^{-6})$ upper complexity bound for first-order smooth problems. This is slower than the optimal $Ω(ε^{-4})$ complexity lower bound in its single-level counterpart. In this work, we show that faster rates are …

Revisit Stochastic Gradient Descent for Strongly Convex Objectives: Tight Uniform-in-Time Bounds
Kang Chen, Yasong Feng, Tianyu Wang
https://arxiv.org/abs/2508.20823 https://

Revisit Stochastic Gradient Descent for Strongly Convex Objectives: Tight Uniform-in-Time Bounds
Stochastic optimization for strongly convex objectives is a fundamental problem in statistics and optimization. This paper revisits the standard Stochastic Gradient Descent (SGD) algorithm for strongly convex objectives and establishes tight uniform-in-time convergence bounds. We prove that with probability larger than $1 - β$, a $\frac{\log \log k + \log (1/β)}{k}$ convergence bound simultaneously holds for all $k \in \mathbb{N}_+$, and show that this rate is tight up to constants. Our resul…

Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods
Yuto Watanabe, Feng-Yi Liao, Yang Zheng
https://arxiv.org/abs/2509.25633 https://

Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods
Robust control seeks stabilizing policies that perform reliably under adversarial disturbances, with $\mathcal{H}_\infty$ control as a classical formulation. It is known that policy optimization of robust $\mathcal{H}_\infty$ control naturally lead to nonsmooth and nonconvex problems. This paper builds on recent advances in nonsmooth optimization to analyze discrete-time static output-feedback $\mathcal{H}_\infty$ control. We show that the $\mathcal{H}_\infty$ cost is weakly convex over any con…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Conditions for representation of a function of many arguments as the difference of convex functions
Igor Proudnikov

On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
https://arxiv.org/abs/2509.13960 https://arx…

On the Moreau envelope properties of weakly convex functions
In this document, we present the main properties satisfied by the Moreau envelope of weakly convex functions. The Moreau envelope has been introduced in convex optimization to regularize convex functionals while preserving their global minimizers. However, the Moreau envelope is also defined for the more general class of weakly convex function and can be a useful tool for optimization in this context. The main properties of the Moreau envelope have been demonstrated for convex functions and are…

Non-Euclidean Broximal Point Method: A Blueprint for Geometry-Aware Optimization
Kaja Gruntkowska, Peter Richt\'arik
https://arxiv.org/abs/2510.00823 https://

Non-Euclidean Broximal Point Method: A Blueprint for Geometry-Aware Optimization
The recently proposed Broximal Point Method (BPM) [Gruntkowska et al., 2025] offers an idealized optimization framework based on iteratively minimizing the objective function over norm balls centered at the current iterate. It enjoys striking global convergence guarantees, converging linearly and in a finite number of steps for proper, closed and convex functions. However, its theoretical analysis has so far been confined to the Euclidean geometry. At the same time, emerging trends in deep lear…

A dynamical formulation of multi-marginal optimal transport
Brendan Pass, Yair Shenfeld
https://arxiv.org/abs/2509.22494 https://arxiv.org/pdf/2509.22494…

A dynamical formulation of multi-marginal optimal transport
We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical dynamical approach of Benamou-Brenier. Our dynamical formulation yields a convex optimization problem, enabling the use of convex optimization tools to find quasi-Monge solutions of the static multi-marginal problem for translation-invariant costs. We illustrate o…

An Optimistic Gradient Tracking Method for Distributed Minimax Optimization
Yan Huang, Jinming Xu, Jiming Chen, Karl Henrik Johansson
https://arxiv.org/abs/2508.21431 https://…

An Optimistic Gradient Tracking Method for Distributed Minimax Optimization
This paper studies the distributed minimax optimization problem over networks. To enhance convergence performance, we propose a distributed optimistic gradient tracking method, termed DOGT, which solves a surrogate function that captures the similarity between local objective functions to approximate a centralized optimistic approach locally. Leveraging a Lyapunov-based analysis, we prove that DOGT achieves linear convergence to the optimal solution for strongly convex-strongly concave objectiv…

Automated algorithm design for convex optimization problems with linear equality constraints
Ibrahim K. Ozaslan, Wuwei Wu, Jie Chen, Tryphon T. Georgiou, Mihailo R. Jovanovic
https://arxiv.org/abs/2509.20746

Automated algorithm design for convex optimization problems with linear equality constraints
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a framework grounded in robust control theory has emerged as a powerful tool for automating algorithm synthesis. By integrating design and analysis stages, fundamental performance bounds are revealed and synthesis of algorithms that achieve them is enabled. In …

Duality between polyhedral approximation of value functions and optimal quantization of measures
Abdellah Bulaich Mehamdi, Wim van Ackooij, Luce Brotcorne, St\'ephane Gaubert, Quentin Jacquet
https://arxiv.org/abs/2509.04101

Duality between polyhedral approximation of value functions and optimal quantization of measures
Approximating a convex function by a polyhedral function that has a limited number of facets is a fundamental problem with applications in various fields, from mitigating the curse of dimensionality in optimal control to bi-level optimization. We establish a connection between this problem and the optimal quantization of a positive measure. Building on recent stability results in optimal transport, by Delalande and Mérigot, we deduce that the polyhedral approximation of a convex function is eq…

First Order Algorithm on an Optimization Problem with Improved Convergence when Problem is Convex
Chee-Khian Sim
https://arxiv.org/abs/2508.13302 https://a…

First Order Algorithm on an Optimization Problem with Improved Convergence when Problem is Convex
We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can be nonsmooth. The algorithm is shown to have an iteration complexity of $\mathcal{O}(ε^{-2})$ to find an $ε$-approximate solution to the problem, and this complexity improves to $\mathcal{O}(ε^{-2/3})$ when the objective function turns out to be convex. W…

Provably data-driven projection method for quadratic programming
Anh Tuan Nguyen, Viet Anh Nguyen
https://arxiv.org/abs/2509.04524 https://arxiv.org/pdf/25…

Provably data-driven projection method for quadratic programming
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs…

Complexity Bounds for Smooth Convex Multiobjective Optimization
Phillipe R. Sampaio
https://arxiv.org/abs/2509.13550 https://arxiv.org/pdf/2509.13550

Complexity Bounds for Smooth Convex Multiobjective Optimization
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. The progress metric is the Pareto stationarity gap $\mathcal{G}(x)$ (the norm of an optimal convex combination of gradients). Our contributions are fourfold. (i) For strongly convex objectives, any span first-order method (iterates lie in the span of past gradients) exhibits linear convergence no faster than $\exp(-Θ(T/\sqrtκ))$ after $T$ oracle calls, wh…

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
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- Gauges and Accelerated Optimization over Smooth and/or Strongly Convex Sets
Ning Liu, Benjamin Grimmer

An Alternating Direction Method of Multipliers for Topology Optimization
Harsh Choudhary, Sven Leyffer, Dominic Yang
https://arxiv.org/abs/2509.19888 https://

An Alternating Direction Method of Multipliers for Topology Optimization
We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design variables, nonsmooth regularization, and non-convex objective renders the problem computationally challenging. To address this, we adopt the alternating direction method of multipliers (ADMM) framework, which enables a decomposition of the original problem int…

Sparse Regularization by Smooth Non-separable Non-convex Penalty Function Based on Ultra-discretization Formula
Natsuki Akaishi, Koki Yamada, Kohei Yatabe
https://arxiv.org/abs/2509.19886

Sparse Regularization by Smooth Non-separable Non-convex Penalty Function Based on Ultra-discretization Formula
In sparse optimization, the $\ell_{1}$ norm is widely adopted for its convexity, yet it often yields solutions with smaller magnitudes than expected. To mitigate this drawback, various non-convex sparse penalties have been proposed. Some employ non-separability, with ordered weighting as an effective example, to retain large components while suppressing small ones. Motivated by these approaches, we propose ULPENS, a non-convex, non-separable sparsity-inducing penalty function that enables contr…

Differential Stochastic Variational Inequalities with Parametric Optimization
Xiaojun Chen, Jian Guo, Guan Wang
https://arxiv.org/abs/2508.15241 https://ar…

Differential Stochastic Variational Inequalities with Parametric Optimization
The differential stochastic variational inequality with parametric convex optimization (DSVI-O) is an ordinary differential equation whose right-hand side involves a stochastic variational inequality and solutions of several dynamic and random parametric convex optimization problems. We consider that the distribution of the random variable is time-dependent and assume that the involved functions are continuous and the expectation is well-defined. We show that the DSVI-O has a weak solution with…

A unified vertical alignment and earthwork model in road design with a new convex optimization model for road networks
Sayan Sadhukhan, Warren Hare, Yves Lucet
https://arxiv.org/abs/2508.15953

A unified vertical alignment and earthwork model in road design with a new convex optimization model for road networks
The vertical alignment optimization problem in road design seeks the optimal vertical alignment of a road at minimal cost, taking into account earthwork while meeting all safety and design requirements. In recent years, modelling techniques have been advanced to incorporate: side slopes, multiple material types, multiple hauling types, and road networks. However, the advancements were created disjointly with implementations that only made a single advancement to the basic model. Herein, we pres…

Sequential Convex Programming with Filtering-Based Warm-Starting for Continuous-Time Multiagent Quadrotor Trajectory Optimization
Minsen Yuan, Yue Yu
https://arxiv.org/abs/2508.14299

Sequential Convex Programming with Filtering-Based Warm-Starting for Continuous-Time Multiagent Quadrotor Trajectory Optimization
Optimizing the trajectories of multiple quadrotors in a shared space is a core challenge in various applications. Many existing trajectory optimization methods enforce constraints only at the discretization points, leading to violations between discretization points. They also often lack warm-starting strategies for iterative solution methods such as sequential convex programming, causing slow convergence or sensitivity to the initial guess. We propose a framework for optimizing multiagent quad…

A Riemannian Accelerated Proximal Gradient Method
Shuailing Feng, Yuhang Jiang, Wen Huang, Shihui Ying
https://arxiv.org/abs/2509.21897 https://arxiv.org/p…

A Riemannian Accelerated Proximal Gradient Method
Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds with theoretical acceleration remains underexplored. To address this issue, we propose a unified Riemannian accelerated proximal gradient method for problems of the form $F(x) = f(x) + h(x)$ on manifolds, where $f$ can be either geodesically convex or geodesica…

Minimization of Nonsmooth Weakly Convex Function over Prox-regular Set for Robust Low-rank Matrix Recovery
Keita Kume, Isao Yamada
https://arxiv.org/abs/2509.17549 https://

Minimization of Nonsmooth Weakly Convex Function over Prox-regular Set for Robust Low-rank Matrix Recovery
We propose a prox-regular-type low-rank constrained nonconvex nonsmooth optimization model for Robust Low-Rank Matrix Recovery (RLRMR), i.e., estimate problem of low-rank matrix from an observed signal corrupted by outliers. For RLRMR, the $\ell_{1}$-norm has been utilized as a convex loss to detect outliers as well as to keep tractability of optimization models. Nevertheless, the $\ell_{1}$-norm is not necessarily an ideal robust loss because the $\ell_{1}$-norm tends to overpenalize entries c…

SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
Zhanwang Deng, Tao Wei, Jirui Ma, Zaiwen Wen
https://arxiv.org/abs/2509.11995 https://…

SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
In this paper, we propose a uniform semismooth Newton-based algorithmic framework called SSNCVX for solving a broad class of convex composite optimization problems. By exploiting the augmented Lagrangian duality, we reformulate the original problem into a saddle point problem and characterize the optimality conditions via a semismooth system of nonlinear equations. The nonsmooth structure is handled internally without requiring problem specific transformation or introducing auxiliary variable…

The Non-Attainment Phenomenon in Robust SOCPs
Vinh Nguyen
https://arxiv.org/abs/2510.00318 https://arxiv.org/pdf/2510.00318

The Non-Attainment Phenomenon in Robust SOCPs
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this crucial guarantee does not extend to Second-Order Cone Programs (SOCPs), a workhorse model in robust and convex optimization. We construct and analyze a rigorous counterexample derived from a robust linear optimization problem with ellipsoidal uncertainty. The re…

Inexact and Stochastic Gradient Optimization Algorithms with Inertia and Hessian Driven Damping
Harsh Choudhary, Jalal Fadili, Vyachelav Kungurtsev
https://arxiv.org/abs/2509.19561

Inexact and Stochastic Gradient Optimization Algorithms with Inertia and Hessian Driven Damping
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can be subject to deterministic and stochastic perturbations. In the deterministic case, we show that under appropriate summability assumptions on the perturbation, our algorithm enjoys fast convergence of the objective values, of the gradients and weak convergenc…

Policy Optimization in the Linear Quadratic Gaussian Problem: A Frequency Domain Perspective
Haoran Li, Xun Li, Yuan-Hua Ni, Xuebo Zhang
https://arxiv.org/abs/2508.17252 https:/…

Policy Optimization in the Linear Quadratic Gaussian Problem: A Frequency Domain Perspective
The Linear Quadratic Gaussian (LQG) problem is a classic and widely studied model in optimal control, providing a fundamental framework for designing controllers for linear systems subject to process and observation noises. In recent years, researchers have increasingly focused on directly parameterizing dynamic controllers and optimizing the LQG cost over the resulting parameterized set. However, this parameterization typically gives rise to a highly non-convex optimization landscape for the r…

Bundle Network: a Machine Learning-Based Bundle Method
Francesca Demelas, Joseph Le Roux, Antonio Frangioni, Mathieu Lacroix, Emiliano Traversi, Roberto Wolfler Calvo
https://arxiv.org/abs/2509.24736

Bundle Network: a Machine Learning-Based Bundle Method
This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth minimization problems. Unlike classical approaches that rely on heuristic tuning of a regularization parameter, our method automatically learns to adjust it from data. Furthermore, we replace the iterative resolution of the optimization problem that provides the search direction-traditionally computed as a convex combination of gradients at visited points-with a recurrent neural mo…

Consensus-Based Optimization Beyond Finite-Time Analysis
Pascal Bianchi (IP Paris, S2A), Alexandru-Radu Dragomir (IP Paris, S2A), Victor Priser (IP Paris, S2A)
https://arxiv.org/abs/2509.12907

Consensus-Based Optimization Beyond Finite-Time Analysis
We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to finite horizons, we investigate its long-time behavior with fixed parameters. In the mean-field limit, a quantitative Laplace principle shows exponential convergence to a neighborhood of the minimizer x * . For finitely many particles, a block-wise analysis y…

Fractional-Order Nesterov Dynamics for Convex Optimization
Tumelo Ranoto
https://arxiv.org/abs/2509.11987 https://arxiv.org/pdf/2509.11987

Fractional-Order Nesterov Dynamics for Convex Optimization
We propose and analyze a class of second-order dynamical systems for continuous-time optimization that incorporate fractional-order gradient terms. The system is given by \begin{equation} \ddot{x}(t) + \fracα{t}\dot{x}(t) + \nabla^θ f(x(t)) = 0, \end{equation} where $θ\in (1,2)$, and the fractional operators are interpreted in the sense of Caputo, Riemann--Liouville, and Grünwald--Letnikov derivatives. This formulation interpolates between memory effects of fractional dynamics and higher-or…

A smoothed proximal trust-region algorithm for nonconvex optimization problems with $L^p$-regularization, $p\in (0,1)$
Harbir Antil, Anna Lentz
https://arxiv.org/abs/2508.15446 …

A smoothed proximal trust-region algorithm for nonconvex optimization problems with $L^p$-regularization, $p\in (0,1)$
We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently by a line search along a suitable proximal path. To handle the nonconvexity and nonsmoothness of the $L^p$-pseudonorm, we replace it by a smooth approximation and construct a convex upper bound of that approximation. This enables us to use results of a trust…