Tootfinder

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Jonathan A. Moran, Pablo G. Morato
https://arxiv.org/abs/2508.18170

Balancing the exploration-exploitation trade-off in active learning for surrogate model-based reliability analysis via multi-objective optimization
Reliability assessment of engineering systems is often hindered by the need to evaluate limit-state functions through computationally expensive simulations, rendering standard sampling impractical. An effective solution is to approximate the limit-state function with a surrogate model iteratively refined through active learning, thereby reducing the number of expensive simulations. At each iteration, an acquisition strategy selects the next sample by balancing two competing goals: exploration, …

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
Xiaoxi Jia, Peter Ochs
https://arxiv.org/abs/2507.18363 https://

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded as a prerequisite, instead, the variable metric is updated by a continuous matrix generator. From the respective of the algorithm, the objective function is approximated by the so-called local model function and subproblems aim to exploit the proximal point(…

Conservative quantum offline model-based optimization
Kristian Sotirov, Annie E. Paine, Savvas Varsamopoulos, Antonio A. Gentile, Osvaldo Simeone
https://arxiv.org/abs/2506.19714 …

Conservative quantum offline model-based optimization
Offline model-based optimization (MBO) refers to the task of optimizing a black-box objective function using only a fixed set of prior input-output data, without any active experimentation. Recent work has introduced quantum extremal learning (QEL), which leverages the expressive power of variational quantum circuits to learn accurate surrogate functions by training on a few data points. However, as widely studied in the classical machine learning literature, predictive models may incorrectly e…

Bayesian preference elicitation for decision support in multiobjective optimization
Felix Huber, Sebastian Rojas Gonzalez, Raul Astudillo
https://arxiv.org/abs/2507.16999

Bayesian preference elicitation for decision support in multiobjective optimization
We present a novel approach to help decision-makers efficiently identify preferred solutions from the Pareto set of a multi-objective optimization problem. Our method uses a Bayesian model to estimate the decision-maker's utility function based on pairwise comparisons. Aided by this model, a principled elicitation strategy selects queries interactively to balance exploration and exploitation, guiding the discovery of high-utility solutions. The approach is flexible: it can be used interactively…

Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach
Deb Narayan Barik, Siddhartha P. Chakrabarty
https://arxiv.org/abs/2507.16494 https://

Can Limited Liability Increase Stability for Banks: A Dynamic Portfolio Approach
We present a novel approach for the bank's decision problem, incorporating Limited Liability in the objective function. Accordingly, we consider continuous time models, with and without Limited Liability. We compare the solutions of these two models to demonstrate the effect of inclusion of Limited Liability. To solve the problem with the objective function incorporating Limited Liability, we approximate the payoff function to another set of functions for which we have closed-form solutions. Th…

Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation
Phurinut Srisawad, Juergen Branke, Long Tran-Thanh
https://arxiv.org/abs/2508.14705 https://

Learning in Repeated Multi-Objective Stackelberg Games with Payoff Manipulation
We study payoff manipulation in repeated multi-objective Stackelberg games, where a leader may strategically influence a follower's deterministic best response, e.g., by offering a share of their own payoff. We assume that the follower's utility function, representing preferences over multiple objectives, is unknown but linear, and its weight parameter must be inferred through interaction. This introduces a sequential decision-making challenge for the leader, who must balance preference elicita…

Online survival analysis with quantile regression
Yi Deng, Shuwei Li, Liuquan Sun, Baoxue Zhang
https://arxiv.org/abs/2507.15696 https://

Online survival analysis with quantile regression
We propose an online inference method for censored quantile regression with streaming data sets. A key strategy is to approximate the martingale-based unsmooth objective function with a quadratic loss function involving a well-justified second-order expansion. This enables us to derive a new online convex function based on the current data batch and summary statistics of historical data, thereby achieving online updating and occupying low storage space. To estimate the regression parameters, we…

Efficient Visual Appearance Optimization by Learning from Prior Preferences
Zhipeng Li, Yi-Chi Liao, Christian Holz
https://arxiv.org/abs/2507.15355 https:…

Efficient Visual Appearance Optimization by Learning from Prior Preferences
Adjusting visual parameters such as brightness and contrast is common in our everyday experiences. Finding the optimal parameter setting is challenging due to the large search space and the lack of an explicit objective function, leaving users to rely solely on their implicit preferences. Prior work has explored Preferential Bayesian Optimization (PBO) to address this challenge, involving users to iteratively select preferred designs from candidate sets. However, PBO often requires many rounds …

An unconditional lower bound for the active-set method in convex quadratic maximization
Eleon Bach, Yann Disser, Sophie Huiberts, Nils Mosis
https://arxiv.org/abs/2507.16648

An unconditional lower bound for the active-set method in convex quadratic maximization
We prove that the active-set method needs an exponential number of iterations in the worst-case to maximize a convex quadratic function subject to linear constraints, regardless of the pivot rule used. This substantially improves over the best previously known lower bound [IPCO 2025], which needs objective functions of polynomial degrees $ω(\log d)$ in dimension $d$, to a bound using a convex polynomial of degree 2. In particular, our result firmly resolves the open question [IPCO 2025] of whe…

The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
Ronny Bergmann, Hajg Jasa, Paula John, Max Pfeffer
https://arxiv.org/abs/2507.16055

The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization
We consider a class of (possibly strongly) geodesically convex optimization problems on Hadamard manifolds, where the objective function splits into the sum of a smooth and a possibly nonsmooth function. We introduce an intrinsic convex Riemannian proximal gradient (CRPG) method that employs the manifold proximal map for the nonsmooth step, without operating in the embedding or tangent space. A sublinear convergence rate for convex problems and a linear convergence rate for strongly convex prob…

Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction
Yubo Sun, Gennian Ge
https://arxiv.org/abs/2508.14386 https://…

Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction
Let $\mathcal{B}(\cdot)$ be an error ball function. A set of $q$-ary sequences of length $n$ is referred to as an \emph{$(n,q,N;\mathcal{B})$-reconstruction code} if each sequence $\boldsymbol{x}$ within this set can be uniquely reconstructed from any $N$ distinct elements within its error ball $\mathcal{B}(\boldsymbol{x})$. The main objective in this area is to determine or establish bounds for the minimum redundancy of $(n,q,N;\mathcal{B})$-reconstruction codes, denoted by $ρ(n,q,N;\mathcal{…

ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters
A. Koley, A. M. Stutz, F. Louvet, F. Motte, A. Ginsburg, R. Galv\'an-Madrid, R. H. \'Alvarez-Guti\'errez, P. Sanhueza, T. Baug, N. Sandoval-Garrido, J. Salinas, G. Busquet, J. Braine, H. -L. Liu, T. Csengeri, A. Gusdorf, M. Fern\'andez-L\'opez, N. Cunningham, L. Bronfman, M. Bonfand

ALMA-IMF XIX: C18O (J=2-1): Measurements of turbulence in 15 massive protoclusters
ALMA-IMF is a large program of the Atacama Large Millimeter/submillimeter Array (ALMA) that aims to determine the origin of the core mass function (CMF) of 15 massive Galactic protoclusters (~ 1.0-25.0 x 10^3 solar mass within ~ 2.5 x 2.5 pc^2 ) located towards the Galactic plane. In addition, the objective of the program is to obtain a thorough understanding of their physical and kinematic properties. Here we study the turbulence in these protoclusters with C18O (2-1) emission line using the s…

Local Differential Privacy for Distributed Stochastic Aggregative Optimization with Guaranteed Optimality
Ziqin Chen, Yongqiang Wang
https://arxiv.org/abs/2506.15106

Local Differential Privacy for Distributed Stochastic Aggregative Optimization with Guaranteed Optimality
Distributed aggregative optimization underpins many cooperative optimization and multi-agent control systems, where each agent's objective function depends both on its local optimization variable and an aggregate of all agents' optimization variables. Existing distributed aggregative optimization approaches typically require access to accurate gradients of the objective functions, which, however, are often hard to obtain in real-world applications. For example, in machine learning, gradients ar…

A new 1D $V_p$ and $V_s$ velocity model of the western Rift of Corinth, Greece, using a fully non-linear tomography algorithm
Mark S. Noble (GEOSCIENCES), Alexandrine Gesret (GEOAZUR 7329), H\'el\`ene Lyon-Caen (GEOAZUR 7329), Anne Deschamps (GEOAZUR 7329)
https://arxiv.org/abs/2506.16222

A new 1D $V_p$ and $V_s$ velocity model of the western Rift of Corinth, Greece, using a fully non-linear tomography algorithm
The objective of this study is to propose a new updated accurate 1-D $V_p$ and $V_s$ velocity model of the western Rift of Corinth for precise absolute earthquake locations. The methodology used to obtain this new model associates two fully non-linear algorithms, a complete exploration of the $V_p$ and $V_s$ model space combined with a grid search method for earthquake locations to minimize the P and S arrival time residuals. We calculated the misfit function for approximately 2.10 6 velocity m…

Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization
Ruihao Zheng, Zhenkun Wang, Yin Wu, Maoguo Gong
https://arxiv.org/abs/2505.21903

Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization
The ideal objective vector, which comprises the optimal values of the $m$ objective functions in an $m$-objective optimization problem, is an important concept in evolutionary multi-objective optimization. Accurate estimation of this vector has consistently been a crucial task, as it is frequently used to guide the search process and normalize the objective space. Prevailing estimation methods all involve utilizing the best value concerning each objective function achieved by the individuals in…

Nonconvex Nonsmooth Multicomposite Optimization and Its Applications to Recurrent Neural Networks
Lingzi Jin, Xiao Wang, Xiaojun Chen
https://arxiv.org/abs/2506.17884

Nonconvex Nonsmooth Multicomposite Optimization and Its Applications to Recurrent Neural Networks
We consider a class of nonconvex nonsmooth multicomposite optimization problems where the objective function consists of a Tikhonov regularizer and a composition of multiple nonconvex nonsmooth component functions. Such optimization problems arise from tangible applications in machine learning and beyond. To define and compute its first-order and second-order d(irectional)-stationary points effectively, we first derive the closed-form expression of the tangent cone for the feasible region of it…

Estimating quantile treatments without strict overlap
Marco Avella-Medina, Richard Davis, Gennady Samorodnitsky
https://arxiv.org/abs/2506.18215 https://…

Estimating quantile treatments without strict overlap
We consider the problem of estimating quantile treatment effects without assuming strict overlap , i.e., we do not assume that the propensity score is bounded away from zero. More specifically, we consider an inverse probability weighting (IPW) approach for estimating quantiles in the potential outcomes framework and pay special attention to scenarios where the propensity scores can tend to zero as a regularly varying function. Our approach effectively considers a heavy-tailed objective functio…

An analysis of the fragmentation function of gluon at next-to-leading order approximation
H. S. Nakhaei, G. R. Boroun
https://arxiv.org/abs/2508.05256 https://

An analysis of the fragmentation function of gluon at next-to-leading order approximation
We are investigating the behavior of the fragmentation function of a gluon, denoted as $ D_{g}(x,μ^2)$, where $μ$ represents the observable scale. This function is derived from the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. Our objective is to evolve the fragmentation function of a gluon for heavy-quark-antiquark bound states with large transverse momentum using a Laplace transform technique. This method enables us to calculate numerical solutions for two and four…

Multi-Tier UAV Edge Computing for Low Altitude Networks Towards Long-Term Energy Stability
Yufei Ye, Shijian Gao, Xinhu Zheng, Liuqing Yang
https://arxiv.org/abs/2508.14601 http…

Multi-Tier UAV Edge Computing for Low Altitude Networks Towards Long-Term Energy Stability
This paper presents a novel multi-tier UAV-assisted edge computing system designed for low-altitude networks. The system comprises vehicle users, lightweight Low-Tier UAVs (L-UAVs), and High-Tier UAV (H-UAV). L-UAVs function as small-scale edge servers positioned closer to vehicle users, while the H-UAV, equipped with more powerful server and larger-capacity battery, serves as mobile backup server to address the limitations in endurance and computing resources of L-UAVs. The primary objective i…

BEASST: Behavioral Entropic Gradient based Adaptive Source Seeking for Mobile Robots
Donipolo Ghimire, Aamodh Suresh, Carlos Nieto-Granda, Solmaz S. Kia
https://arxiv.org/abs/2508.10363

BEASST: Behavioral Entropic Gradient based Adaptive Source Seeking for Mobile Robots
This paper presents BEASST (Behavioral Entropic Gradient-based Adaptive Source Seeking for Mobile Robots), a novel framework for robotic source seeking in complex, unknown environments. Our approach enables mobile robots to efficiently balance exploration and exploitation by modeling normalized signal strength as a surrogate probability of source location. Building on Behavioral Entropy(BE) with Prelec's probability weighting function, we define an objective function that adapts robot behavior …

An End-to-End Multi-objective Ensemble Ranking Framework for Video Recommendation
Tiantian He, Minzhi Xie, Runtong Li, Xiaoxiao Xu, Jiaqi Yu, Zixiu Wang, Lantao Hu, Han Li, Kun Gai
https://arxiv.org/abs/2508.05093

An End-to-End Multi-objective Ensemble Ranking Framework for Video Recommendation
We propose a novel End-to-end Multi-objective Ensemble Ranking framework (EMER) for the multi-objective ensemble ranking module, which is the most critical component of the short video recommendation system. EMER enhances personalization by replacing manually-designed heuristic formulas with an end-to-end modeling paradigm. EMER introduces a meticulously designed loss function to address the fundamental challenge of defining effective supervision for ensemble ranking, where no single ground-tru…

Three-Dimensional Isotropic STED Nanoscopy using a Single Objective
Renlong Zhang, Xiaoyu Weng, Haoxian Zhou, Luwei Wang, Fangrui Lin, Wei Yan, Xiumin Gao, Bin Yu, Danying Lin, Liwei Liu, Chenshuang Zhang, Kayla K. Green, Ewoud R. E. Schmidt, Songlin Zhuang, Junle Qu
https://arxiv.org/abs/2507.06718

Three-Dimensional Isotropic STED Nanoscopy using a Single Objective
Accurate three-dimensional (3D) imaging requires an isotropic point spread function (PSF). However, the inherent missing aperture of a single objective lens results in an elongated, cigar-like PSF, which has rendered isotropic resolution in fluorescence microscopy seemingly insurmountable without a 4π configuration for decades. To address this long-standing challenge, we introduce ISO-STED (Isotropic Single-Objective STED) Nanoscopy, a novel approach that employs a single objective lens and a …

S2WTM: Spherical Sliced-Wasserstein Autoencoder for Topic Modeling
Suman Adhya, Debarshi Kumar Sanyal
https://arxiv.org/abs/2507.12451 https://

S2WTM: Spherical Sliced-Wasserstein Autoencoder for Topic Modeling
Modeling latent representations in a hyperspherical space has proven effective for capturing directional similarities in high-dimensional text data, benefiting topic modeling. Variational autoencoder-based neural topic models (VAE-NTMs) commonly adopt the von Mises-Fisher prior to encode hyperspherical structure. However, VAE-NTMs often suffer from posterior collapse, where the KL divergence term in the objective function highly diminishes, leading to ineffective latent representations. To miti…

Frank-Wolfe algorithm for star-convex functions
R. Diaz Millan, Orizon Pereira Ferreira, Julien Ugon
https://arxiv.org/abs/2507.17272 https://arxiv.org/pdf…

Frank-Wolfe algorithm for star-convex functions
We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of \emph{star-convex functions}, which retain essential geometric properties despite the lack of convexity. We establish iteration-complexity bounds of $\mathcal{O}(1/k)$ for both the objective values and the duality gap under star-convexity, using diminishing, Armijo…

Dynamic Regret Reduces to Kernelized Static Regret
Andrew Jacobsen, Alessandro Rudi, Francesco Orabona, Nicolo Cesa-Bianchi
https://arxiv.org/abs/2507.05478

Dynamic Regret Reduces to Kernelized Static Regret
We study dynamic regret in online convex optimization, where the objective is to achieve low cumulative loss relative to an arbitrary benchmark sequence. By observing that competing with an arbitrary sequence of comparators $u_{1},\ldots,u_{T}$ in $\mathcal{W}\subseteq\mathbb{R}^{d}$ is equivalent to competing with a fixed comparator function $u:[1,T]\to \mathcal{W}$, we frame dynamic regret minimization as a static regret problem in a function space. By carefully constructing a suitable functi…

Single and multi-objective optimal designs for group testing experiments
Chi-Kuang Yeh, Weng Kee Wong, Julie Zhou
https://arxiv.org/abs/2508.08445 https://…

Single and multi-objective optimal designs for group testing experiments
Group testing, or pooled sample testing, is an active research area with increasingly diverse applications across disciplines. This paper considers design issues for group testing problems when a statistical model, an optimality criterion and a cost function are given. We use the software CVX to find designs that best estimate all or some of the model parameters ($D$ -, $D_s$ -, $A$-optimality) when there is one or more objectives in the study. A novel feature is that we include maximin types o…

A shape optimisation of mutual inductances among coils
Toru Takahashi, Tatsuya Tokito, Yi Cui, Toshiro Matsumoto
https://arxiv.org/abs/2506.14085 https://

A shape optimisation of mutual inductances among coils
This paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using B-spline curves, with control points (CPs) serving as design variables. The key contribution is the derivation of the shape derivative of the objective function in terms of MIs, enabling the use of gradient-based quasi-Newton optimisation methods. A coil length constraint is also incorporated. The study …

An Efficient Network-aware Direct Search Method for Influence Maximization
Matteo Bergamaschi, Sara Venturini, Francesco Tudisco, Francesco Rinaldi
https://arxiv.org/abs/2508.12164

An Efficient Network-aware Direct Search Method for Influence Maximization
Influence Maximization (IM) is a pivotal concept in social network analysis, involving the identification of influential nodes within a network to maximize the number of influenced nodes, and has a wide variety of applications that range from viral marketing and information dissemination to public health campaigns. IM can be modeled as a combinatorial optimization problem with a black-box objective function, where the goal is to select $B$ seed nodes that maximize the expected influence spread.…

The Generalized Matrix Separation Problem: Algorithms
Xuemei Chen, Owen Deen
https://arxiv.org/abs/2507.17069 https://arxiv.org/pdf/2507.17069

The Generalized Matrix Separation Problem: Algorithms
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is the sum of the $\ell_1$-norm and nuclear norm. In this paper we detail the iterative algorithms and its associated computations for solving this convex optimization problem. We present various efficient implementation strategies, with attention to practical ca…

Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization
Ruihao Zheng, Zhenkun Wang, Yin Wu, Maoguo Gong
https://arxiv.org/abs/2505.21903

Enhanced Ideal Objective Vector Estimation for Evolutionary Multi-Objective Optimization
The ideal objective vector, which comprises the optimal values of the $m$ objective functions in an $m$-objective optimization problem, is an important concept in evolutionary multi-objective optimization. Accurate estimation of this vector has consistently been a crucial task, as it is frequently used to guide the search process and normalize the objective space. Prevailing estimation methods all involve utilizing the best value concerning each objective function achieved by the individuals in…

GLASD: A Loss-Function-Agnostic Global Optimizer for Robust Correlation Estimation under Data Contamination and Heavy Tails
Priyam Das
https://arxiv.org/abs/2506.14801

GLASD: A Loss-Function-Agnostic Global Optimizer for Robust Correlation Estimation under Data Contamination and Heavy Tails
Robust correlation estimation is essential in high-dimensional settings, particularly when data are contaminated by outliers or exhibit heavy-tailed behavior. Many robust loss functions of practical interest-such as those involving truncation or redescending M-estimators-lead to objective functions that are inherently non-convex and non-differentiable. Traditional methods typically focus on a single loss function tailored to a specific contamination model and develop custom algorithms tightly c…

Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees
Max L. N. Goncalves, Geovani N. Grapiglia
https://arxiv.org/abs/2507.17556 https://

Sub-sampled Trust-Region Methods with Deterministic Worst-Case Complexity Guarantees
In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function, significantly reducing the overall computational cost. We propose a novel adaptive procedure for deterministically adjusting the sample size used for gradient (or gradient and Hessian) approximations. Furthermore, we establish worst-case iteration complexity bounds for o…

Constraint Optimized Multichannel Mixer-limiter Design
Yuancheng Luo, Dmitriy Yamkovoy, Guillermo Garcia
https://arxiv.org/abs/2507.06769 https://

Constraint Optimized Multichannel Mixer-limiter Design
Multichannel audio mixer and limiter designs are conventionally decoupled for content reproduction over loudspeaker arrays due to high computational complexity and run-time costs. We propose a coupled mixer-limiter-envelope design formulated as an efficient linear-constrained quadratic program that minimizes a distortion objective over multichannel gain variables subject to sample mixture constraints. Novel methods for asymmetric constant overlap-add window optimization, objective function appr…

Adaptive Data Augmentation for Thompson Sampling
Wonyoung Kim
https://arxiv.org/abs/2506.14479 https://arxiv.org/pdf/2506.14479

Adaptive Data Augmentation for Thompson Sampling
In linear contextual bandits, the objective is to select actions that maximize cumulative rewards, modeled as a linear function with unknown parameters. Although Thompson Sampling performs well empirically, it does not achieve optimal regret bounds. This paper proposes a nearly minimax optimal Thompson Sampling for linear contextual bandits by developing a novel estimator with the adaptive augmentation and coupling of the hypothetical samples that are designed for efficient parameter learning. …

A trust-region framework for optimization using Hermite kernel surrogate models
Sven Ullmann, Tobias Ehring, Robin Herkert, Bernard Haasdonk
https://arxiv.org/abs/2507.01729

A trust-region framework for optimization using Hermite kernel surrogate models
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often impractical due to expensive function evaluations. To address these challenges, we leverage a trust-region strategy, where the objective function is approximated by an efficient surrogate model within a local neighborhood of the current iterate. In particula…

ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning
Rahel Rickenbach, Alan A. Lahoud, Erik Schaffernicht, Melanie N. Zeilinger, Johannes A. Stork
https://arxiv.org/abs/2507.13088

ZipMPC: Compressed Context-Dependent MPC Cost via Imitation Learning
The computational burden of model predictive control (MPC) limits its application on real-time systems, such as robots, and often requires the use of short prediction horizons. This not only affects the control performance, but also increases the difficulty of designing MPC cost functions that reflect the desired long-term objective. This paper proposes ZipMPC, a method that imitates a long-horizon MPC behaviour by learning a compressed and context-dependent cost function for a short-horizon MP…

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…

Decoupling Geometry from Optimization in 2D Irregular Cutting and Packing Problems: an Open-Source Collision Detection Engine
Jeroen Gardeyn, Tony Wauters, Greet Vanden Berghe
https://arxiv.org/abs/2508.08341

Decoupling Geometry from Optimization in 2D Irregular Cutting and Packing Problems: an Open-Source Collision Detection Engine
Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether or not an item can be placed feasibly at a certain position, and the optimization challenge of finding a good solution according to some objective function. Until now, those tackling such problems have had to address both challenges simultaneously, requiring two distinct sets of expertise and a lot of research & development effort. One way to lower t…

This https://arxiv.org/abs/2412.17780 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

PepTune: De Novo Generation of Therapeutic Peptides with Multi-Objective-Guided Discrete Diffusion
We present PepTune, a multi-objective discrete diffusion model for simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with a novel bond-dependent masking schedule and invalid loss function. To guide the diffusion process, we introduce Monte Carlo Tree Guidance (MCTG), an inference-time multi-objective guidance algorithm that balances exploration and exploitation to iterati…

An Optimization-Based Framework for Solving Forward-Backward Stochastic Differential Equations: Convergence Analysis and Error Bounds
Yutian Wang, Yuan-Hua Ni, Xun Li
https://arxiv.org/abs/2507.15234

An Optimization-Based Framework for Solving Forward-Backward Stochastic Differential Equations: Convergence Analysis and Error Bounds
In this paper, we develop an optimization-based framework for solving coupled forward-backward stochastic differential equations. We introduce an integral-form objective function and prove its equivalence to the error between consecutive Picard iterates. Our convergence analysis establishes that minimizing this objective generates sequences that converge to the true solution. We provide explicit upper and lower bounds that relate the objective value to the error between trial and exact solution…

Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction
Nico Meyer, Christopher Mutschler, Andreas Maier, Daniel D. Scherer
https://arxiv.org/abs/2506.11552

Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We propose a novel objective function for tailoring error correction codes to specific noise structures by maximizing the distinguishability between quantum states after a noise channel, ensuring efficient recovery operations. We formalize this concept with the distin…

Array-Aware Ambisonics and HRTF Encoding for Binaural Reproduction With Wearable Arrays
Yhonatan Gayer, Vladimir Tourbabin, Zamir Ben Hur, David Lou Alon, Boaz Rafaely
https://arxiv.org/abs/2507.11091

Array-Aware Ambisonics and HRTF Encoding for Binaural Reproduction With Wearable Arrays
This work introduces a novel method for binaural reproduction from arbitrary microphone arrays, based on array-aware optimization of Ambisonics encoding through Head-Related Transfer Function (HRTF) pre-processing. The proposed approach integrates array-specific information into the HRTF processing pipeline, leading to improved spatial accuracy in binaural rendering. Objective evaluations demonstrate superior performance under simulated wearable-array and head rotations compared to conventional…

Inference on the value of linear programs
Leonard Goff, Eric Mbakop
https://arxiv.org/abs/2506.06776 https://arxiv.org/pdf/2506.06776…

Inference on the value of linear programs
This paper studies inference on the value of linear programs (LPs) when both the objective function and constraints are possibly unknown and must be estimated from data. We show that many inference problems in partially identified models can be reformulated in this way. Building on Shapiro (1991) and Fang and Santos (2019), we develop a pointwise valid inference procedure for the value of LPs. We modify this pointwise inference procedure to construct one-sided inference procedures that are unif…

Experimental Scheme for Polarizing the Boron Nuclei
William R. Milner, Richard G. Milner
https://arxiv.org/abs/2508.06561 https://arxiv.org/pdf/2508.06561

Experimental Scheme for Polarizing the Boron Nuclei
Unravelling the internal structure of hadrons and nuclei in terms of the quarks and gluons of Quantum Chromodynamics is a central focus of current nuclear physics research. Directly observing gluonic states in the nucleus would be groundbreaking and is an objective of the future Electron-Ion Collider (EIC). Over thirty years ago, Jaffe and Manohar identified a new double-helicity flip structure function, directly sensitive to exotic gluons. They pointed out that this could be measured in inclus…

The pursuit of happiness
Debora Princepe, Onofrio Mazzarisi, Erol Akcay, Simon A. Levin, Matteo Marsili
https://arxiv.org/abs/2506.10537 https://

The pursuit of happiness
Happiness, in the U.S. Declaration of Independence, was understood quite differently from today's popular notions of personal pleasure. Happiness implies a flourishing life - one of virtue, purpose, and contribution to the common good. This paper studies populations of individuals - that we call homo-felix - who maximise an objective function that we call happiness. The happiness of one individual depends on the payoffs that they receive in games they play with their peers as well as on the hap…

Inverse Optimal Control with Constraint Relaxation
Rahel Rickenbach, Amon Lahr, Melanie N. Zeilinger
https://arxiv.org/abs/2507.11392 https://

Inverse Optimal Control with Constraint Relaxation
Inverse optimal control (IOC) is a promising paradigm for learning and mimicking optimal control strategies from capable demonstrators, or gaining a deeper understanding of their intentions, by estimating an unknown objective function from one or more corresponding optimal control sequences. When computing estimates from demonstrations in environments with safety-preserving inequality constraints, acknowledging their presence in the chosen IOC method is crucial given their strong influence on t…

Unrolling Nonconvex Graph Total Variation for Image Denoising
Songlin Wei, Gene Cheung, Fei Chen, Ivan Selesnick
https://arxiv.org/abs/2506.02381 https://

Unrolling Nonconvex Graph Total Variation for Image Denoising
Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable …

On the Effect of Instruction Tuning Loss on Generalization
Anwoy Chatterjee, H S V N S Kowndinya Renduchintala, Sumit Bhatia, Tanmoy Chakraborty
https://arxiv.org/abs/2507.07817

On the Effect of Instruction Tuning Loss on Generalization
Instruction Tuning has emerged as a pivotal post-training paradigm that enables pre-trained language models to better follow user instructions. Despite its significance, little attention has been given to optimizing the loss function used. A fundamental, yet often overlooked, question is whether the conventional auto-regressive objective - where loss is computed only on response tokens, excluding prompt tokens - is truly optimal for instruction tuning. In this work, we systematically investigat…

Kurdyka-\L ojasiewicz exponent via sqaure parametrization
Wenqing Ouyang
https://arxiv.org/abs/2506.10110 https://arxiv.org/pdf/2506.…

Kurdyka-Łojasiewicz exponent via sqaure parametrization
We consider one of the most common reparameterization techniques, the square transformation. Assuming the original objective function is the sum of a smooth function and a polyhedral function, we study the variational properties of the objective function after reparameterization. In particular, we first study the minimal norm of the subdifferential of the reparameterized objective function. Second, we compute the second subderivative of the reparameterized objective function on a linear subspac…

Solving Distance-Based Optimization Problems Using Optical Hardware
Guangyao Li, Richard Zhipeng Wang, Natalia G. Berloff
https://arxiv.org/abs/2507.11378 …

Solving Distance-Based Optimization Problems Using Optical Hardware
We present a practical approach to solving distance-based optimization problems using optical computing hardware. The objective is to minimize an energy function defined as the weighted sum of squared differences between measured distances and the squared Euclidean distances of point coordinates. By representing coordinates as complex numbers, we map the optimization problem onto optical fields, enabling its solution through either the canonical transformation (CT) method or the gain-based bifu…

Multi-Objective Covariance Matrix Adaptation MAP-Annealing
Shihan Zhao, Stefanos Nikolaidis
https://arxiv.org/abs/2505.20712 https://…

Multi-Objective Covariance Matrix Adaptation MAP-Annealing
Quality-Diversity (QD) optimization is an emerging field that focuses on finding a set of behaviorally diverse and high-quality solutions. While the quality is typically defined w.r.t. a single objective function, recent work on Multi-Objective Quality-Diversity (MOQD) extends QD optimization to simultaneously optimize multiple objective functions. This opens up multi-objective applications for QD, such as generating a diverse set of game maps that maximize difficulty, realism, or other propert…

Guidelines for Gaze-based Neural Preliminary Diagnosis
Mayar Elfares, Salma Younis, Pascal Reisert, Ralf K\"usters, Tobias Renner, Andreas Bulling
https://arxiv.org/abs/2506.08517

Guidelines for Gaze-based Neural Preliminary Diagnosis
Neural disorders refer to any condition affecting the nervous system and that influence how individuals perceive and interact with the world. Traditional neural diagnoses rely on cumbersome, time-consuming, or subjective methods, such as clinical interviews, behavioural observations, or medical imaging. Eye tracking is an attractive alternative because analysing eye movements, such as fixations and saccades, can provide more objective insights into brain function and cognitive processing by cap…

Thompson Sampling in Function Spaces via Neural Operators
Rafael Oliveira, Xuesong Wang, Kian Ming A. Chai, Edwin V. Bonilla
https://arxiv.org/abs/2506.21894

Thompson Sampling in Function Spaces via Neural Operators
We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity simulator) are costly. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approxi…

A Distributional View of High Dimensional Optimization
Felix Benning
https://arxiv.org/abs/2507.16315 https://arxiv.org/pdf/2507.1631…

A Distributional View of High Dimensional Optimization
This PhD thesis presents a distributional view of optimization in place of a worst-case perspective. We motivate this view with an investigation of the failure point of classical optimization. Subsequently we consider the optimization of a randomly drawn objective function. This is the setting of Bayesian Optimization. After a review of Bayesian optimization we outline how such a distributional view may explain predictable progress of optimization in high dimension. It further turns out that th…

Quantile Reward Policy Optimization: Alignment with Pointwise Regression and Exact Partition Functions
Simon Matrenok, Skander Moalla, Caglar Gulcehre
https://arxiv.org/abs/2507.08068 https://arxiv.org/pdf/2507.08068 https://arxiv.org/html/2507.08068
arXiv:2507.08068v1 Announce Type: new
Abstract: Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are limited to learning from preference pairs or relative signals. To bridge this gap, we introduce \emph{Quantile Reward Policy Optimization} (QRPO), which learns from pointwise absolute rewards while preserving the simplicity and offline applicability of DPO-like methods. QRPO uses quantile rewards to enable regression to the closed-form solution of the KL-regularized RL objective. This reward yields an analytically tractable partition function, removing the need for relative signals to cancel this term. Moreover, QRPO scales with increased compute to estimate quantile rewards, opening a new dimension for pre-computation scaling. Empirically, QRPO consistently achieves top performance on chat and coding evaluations -- reward model scores, AlpacaEval 2, and LeetCode -- compared to DPO, REBEL, and SimPO across diverse datasets and 8B-scale models. Finally, we find that training with robust rewards instead of converting them to preferences induces less length bias.
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Multi-Objective Covariance Matrix Adaptation MAP-Annealing
Shihan Zhao, Stefanos Nikolaidis
https://arxiv.org/abs/2505.20712 https://…

Multi-Objective Covariance Matrix Adaptation MAP-Annealing
Quality-Diversity (QD) optimization is an emerging field that focuses on finding a set of behaviorally diverse and high-quality solutions. While the quality is typically defined w.r.t. a single objective function, recent work on Multi-Objective Quality-Diversity (MOQD) extends QD optimization to simultaneously optimize multiple objective functions. This opens up multi-objective applications for QD, such as generating a diverse set of game maps that maximize difficulty, realism, or other propert…

A Generalized $\ell_1$-Merit Function SQP Method Using Function Approximations with Tunable Accuracy
Dane S. Grundvig, Matthias Heinkenschloss
https://arxiv.org/abs/2507.06199

A Generalized $\ell_1$-Merit Function SQP Method Using Function Approximations with Tunable Accuracy
This paper develops a generalization of the line-search sequential quadratic programming (SQP) algorithm with $\ell_1$-merit function that uses objective and constraint function approximations with tunable accuracy to solve smooth equality-constrained optimization problems. The evaluation of objective and constraint functions and their gradients is potentially computationally expensive, but it is assumed that one can construct effective, computationally inexpensive models of these functions. Th…

Toroidal area-preserving parameterizations of genus-one closed surfaces
Marco Sutti, Mei-Heng Yueh
https://arxiv.org/abs/2508.05111 https://arxiv.org/pdf/2…

Toroidal area-preserving parameterizations of genus-one closed surfaces
We consider the problem of computing toroidal area-preserving parameterizations of genus-one closed surfaces. We propose four algorithms based on Riemannian geometry: the projected gradient descent method, the projected conjugate gradient method, the Riemannian gradient method, and the Riemannian conjugate gradient method. Our objective function is based on the stretch energy functional, and the minimization is constrained on a power manifold of ring tori embedded in three-dimensional Euclidean…

WhiSQA: Non-Intrusive Speech Quality Prediction Using Whisper Encoder Features
George Close, Kris Hong, Thomas Hain, Stefan Goetze
https://arxiv.org/abs/2508.02210 https://

WhiSQA: Non-Intrusive Speech Quality Prediction Using Whisper Encoder Features
There has been significant research effort developing neural-network-based predictors of SQ in recent years. While a primary objective has been to develop non-intrusive, i.e.~reference-free, metrics to assess the performance of SE systems, recent work has also investigated the direct inference of neural SQ predictors within the loss function of downstream speech tasks. To aid in the training of SQ predictors, several large datasets of audio with corresponding human labels of quality have been c…

Distributionally Robust Control with Constraints on Linear Unidimensional Projections
Alexandros E. Tzikas, Lukas Fiechtner, Arec Jamgochian, Mykel J. Kochenderfer
https://arxiv.org/abs/2508.07121

Distributionally Robust Control with Constraints on Linear Unidimensional Projections
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution from an ambiguity set. We consider an interpretable and expressive class of ambiguity sets defined by constraints on the expected value of functions of one-dimensional linear projections of the uncertain parameters. Prior work has shown that, under conditions,…

Physics-Informed Neural Network Approach to Quark-Antiquark Color Flux Tube
Wei Kou, Xiaoxuan Lin, Bing'ang Guo, Xurong Chen
https://arxiv.org/abs/2506.03513

Physics-Informed Neural Network Approach to Quark-Antiquark Color Flux Tube
We introduce a physics-informed neural network (PINNs) framework for modelling the spatial distribution of chromodynamic fields induced by quark-antiquark pairs, based on lattice Monte Carlo simulations. In contrast to conventional neural networks, PINNs incorporate physical laws--expressed here as differential equations governing type-II superconductivity--directly into the training objective. By embedding these equations into the loss function, we guide the network to learn physically consist…

A bang-bang solution with infinitely many switching points for a parabolic boundary control problem with terminal observation
Constantin Christof
https://arxiv.org/abs/2506.12768 …

A bang-bang solution with infinitely many switching points for a parabolic boundary control problem with terminal observation
We study a parabolic boundary control problem with one spatial dimension, control constraints of box type, and an objective function that measures the $L^2$-distance to a desired terminal state. It is shown that, for a certain choice of the desired state, the considered problem possesses an optimal control that is chattering, i.e., of bang-bang type with infinitely many switching points and a positive objective function value. Whether such a solution is possible has been an open question in the…

A Robust Optimization Framework for Flexible Industrial Energy Scheduling: Application to a Cement Plant with Market Participation
Sebasti\'an Rojas-Innocenti, Enrique Baeyens, Alejandro Mart\'in-Crespo, Sergio Saludes-Rodil, Fernando Frechoso Escudero
https://arxiv.org/abs/2506.10824

A Robust Optimization Framework for Flexible Industrial Energy Scheduling: Application to a Cement Plant with Market Participation
This paper presents a scenario based robust optimization framework for short term energy scheduling in electricity intensive industrial plants, explicitly addressing uncertainty in planning decisions. The model is formulated as a two-stage Mixed Integer Linear Program (MILP) and integrates a hybrid scenario generation method capable of representing uncertain inputs such as electricity prices, renewable generation, and internal demand. A convex objective function combining expected and worst cas…

Lyapunov analysis for FISTA under strong convexity
Luis M. Brice\~no-Arias
https://arxiv.org/abs/2506.11785 https://arxiv.org/pdf/250…

Lyapunov analysis for FISTA under strong convexity
In this paper, we conduct a theoretical and numerical study of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) under strong convexity assumptions. We propose an autonomous Lyapunov function that reflects the strong convexity of the objective function, whether it arises from the smooth or non-smooth component. This Lyapunov function decreases monotonically at a linear rate along the iterations of the algorithm for a fixed inertial parameter. Our analysis demonstrates that the best th…

EXPO: Stable Reinforcement Learning with Expressive Policies
Perry Dong, Qiyang Li, Dorsa Sadigh, Chelsea Finn
https://arxiv.org/abs/2507.07986 https://arxiv.org/pdf/2507.07986 https://arxiv.org/html/2507.07986
arXiv:2507.07986v1 Announce Type: new
Abstract: We study the problem of training and fine-tuning expressive policies with online reinforcement learning (RL) given an offline dataset. Training expressive policy classes with online RL present a unique challenge of stable value maximization. Unlike simpler Gaussian policies commonly used in online RL, expressive policies like diffusion and flow-matching policies are parameterized by a long denoising chain, which hinders stable gradient propagation from actions to policy parameters when optimizing against some value function. Our key insight is that we can address stable value maximization by avoiding direct optimization over value with the expressive policy and instead construct an on-the-fly RL policy to maximize Q-value. We propose Expressive Policy Optimization (EXPO), a sample-efficient online RL algorithm that utilizes an on-the-fly policy to maximize value with two parameterized policies -- a larger expressive base policy trained with a stable imitation learning objective and a light-weight Gaussian edit policy that edits the actions sampled from the base policy toward a higher value distribution. The on-the-fly policy optimizes the actions from the base policy with the learned edit policy and chooses the value maximizing action from the base and edited actions for both sampling and temporal-difference (TD) backup. Our approach yields up to 2-3x improvement in sample efficiency on average over prior methods both in the setting of fine-tuning a pretrained policy given offline data and in leveraging offline data to train online.
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Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Paul N. Patrone, Anthony J. Kearsley
https://arxiv.org/abs/2508.01065 h…

Inequalities for Optimization of Classification Algorithms: A Perspective Motivated by Diagnostic Testing
Motivated by canonical problems in medical diagnostics, we propose and study properties of an objective function that uniformly bounds uncertainties in quantities of interest extracted from classifiers and related data analysis tools. We begin by adopting a set-theoretic perspective to show how two main tasks in diagnostics -- classification and prevalence estimation -- can be recast in terms of a variation on the confusion (or error) matrix ${\boldsymbol {\rm P}}$ typically considered in super…

This https://arxiv.org/abs/2505.21356 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSD_…

Towards Robust Automated Perceptual Voice Quality Assessment with Deep Learning
Objective: Perceptual voice quality assessment plays a critical role in diagnosing and monitoring voice disorders by providing standardized evaluation of vocal function. Traditionally, this process relies on expert raters utilizing standard scales, such as the Consensus Auditory-Perceptual Evaluation of Voice (CAPE-V) and Grade, Roughness, Breathiness, Asthenia, and Strain (GRBAS). However, these metrics are inherently subjective and susceptible to inter-rater variability, motivating the need f…

Non-linear Multi-objective Optimization with Probabilistic Branch and Bound
Hao Huang, Zelda B. Zabinsky
https://arxiv.org/abs/2506.04554 https://

Non-linear Multi-objective Optimization with Probabilistic Branch and Bound
A multiple objective simulation optimization algorithm named Multiple Objective Probabilistic Branch and Bound with Single Observation (MOPBnB(so)) is presented for approximating the Pareto optimal set and the associated efficient frontier for stochastic multi-objective optimization problems. MOPBnB(so) evaluates a noisy function exactly once at any solution and uses neighboring solutions to estimate the objective functions, in contrast to a variant that uses multiple replications at a solution…

Optimal Task Offloading with Firm Deadlines for Mobile Edge Computing Systems
Khai Doan, Wesley Araujo, Evangelos Kranakis, Ioannis Lambadaris, Yannis Viniotis, Wonjae Shin
https://arxiv.org/abs/2506.09180

Optimal Task Offloading with Firm Deadlines for Mobile Edge Computing Systems
Under a dramatic increase in mobile data traffic, a promising solution for edge computing systems to maintain their local service is the task migration that may be implemented by means of Autonomous mobile agents (AMA). In designing an optimal scheme for task offloading to AMA, we define a system cost as a minimization objective function that comprises two parts. First, an offloading cost which can be interpreted as the cost of using computational resources from the AMA. Second, a penalty cost …

Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity
Jingfan Xia, Zhenwei Lin, Qi Deng
https://arxiv.org/abs/2508.13496 https://

Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity
Randomized smoothing is a widely adopted technique for optimizing nonsmooth objective functions. However, its efficiency analysis typically relies on global Lipschitz continuity, a condition rarely met in practical applications. To address this limitation, we introduce a new subgradient growth condition that naturally encompasses a wide range of locally Lipschitz functions, with the classical global Lipschitz function as a special case. Under this milder condition, we prove that randomized smoo…

A DC-Reformulation for Gradient-$L^0$-Constrained Problems in Function Spaces
Bastian Dittrich, Evelyn Herberg, Roland Herzog, Georg M\"uller
https://arxiv.org/abs/2506.11917

A DC-Reformulation for Gradient-$L^0$-Constrained Problems in Function Spaces
Cardinality constraints in optimization are commonly of $L^0$-type, and they lead to sparsely supported optimizers. An efficient way of dealing with these constraints algorithmically, when the objective functional is convex, is reformulating the constraint using the difference of suitable $L^1$- and largest-$K$-norms and subsequently solving a sequence of penalized subproblems in the difference-of-convex (DC) class. We extend this DC-reformulation approach to problems with $L^0$-type cardinalit…

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
Jonathan R. Cangelosi, Matthias Heinkenschloss
https://arxiv.org/abs/2506.10804

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
This work establishes sensitivities of the solution of an optimal control problem (OCP) and a corresponding quantity of interest (QoI) to perturbations in a state/control-dependent component function that appears in the governing ODEs and the objective function. This extends existing OCP sensitivity results, which consider the sensitivity of the OCP solution with respect to state/control-independent parameters. It is shown that with Carathéodory-type assumptions, the Implicit Function Theorem …

Economic Model Predictive Control with a Non-Fixed Reference Trajectory for Optimal Microgrid Dispatch
Avik Ghosh, Adil Khurram, Jan Kleissl, Sonia Martinez
https://arxiv.org/abs/2506.22406

Economic Model Predictive Control with a Non-Fixed Reference Trajectory for Optimal Microgrid Dispatch
Economic Model Predictive Control (EMPC), instead of stabilizing a reference trajectory/state in the objective function like a Tracking MPC, optimizes the economic performance over the prediction horizon, making it attractive for economical microgrid (MG) dispatch. However, the demand charge component in the monthly electricity cost, make it difficult to be encapsulated in additive stage costs, and can make solutions violate the principle of optimality if naively introduced in the objective fun…

Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the {\L}ojasiewicz condition
Vassilis Apidopoulos, Vasiliki Mavrogeorgou, Theodoros G. Tsironis
https://arxiv.org/abs/2506.11705

Heavy-ball dynamics with Hessian-driven damping for non-convex optimization under the Łojasiewicz condition
In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a Łojasiewicz condition. In this general setting, we provide a series of tight, worst-case optimal convergence rate guarantees as a function of the dynamics' friction coefficients and the Łojasiewicz exponent of the problem's objective function. Importantly, the linear rates that we obtain improve on previous available rates and they sug…

Global Descent Method for Non-convex Multi-objective Optimization Problems
Bikram Adhikary, Md Abu Talhamainuddin Ansary, Savin Treanta
https://arxiv.org/abs/2507.22390 https://…

Global Descent Method for Non-convex Multi-objective Optimization Problems
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for predefined scalars or ordering information of objective functions. Initially, the proposed method identifies a local weak efficient solution using any suitable descent algorithm, then applies an auxiliary function termed the multi-objective global descent functio…

BSDE Approach for $\alpha$-Potential Stochastic Differential Games
Xin Guo, Xun Li, Liangquan Zhang
https://arxiv.org/abs/2507.13256 https://

BSDE Approach for $α$-Potential Stochastic Differential Games
In this paper, we examine a class of $α$-potential stochastic differential games with random coefficients via the backward stochastic differential equations (BSDEs) approach. Specifically, we show that the first and second order linear derivatives of the objective function for each player can be expressed through the corresponding first and second-order adjoint equations, which leads to rigorous estimates for $α$. We illustrate the dependence of $α$ on game characteristics through detailed a…

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization
Serge Gratton, Alena Kopani\v{c}\'akov\'a, Philippe Toint
https://arxiv.org/abs/2507.11513

Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization
Two OFFO (Objective-Function Free Optimization) noise tolerant algorithms are presented that handle bound constraints, inexact gradients and use second-order information when available.The first is a multi-level method exploiting a hierarchical description of the problem and the second is a domain-decomposition method covering the standard addditive Schwarz decompositions. Both are generalizations of the first-order AdaGrad algorithm for unconstrained optimization. Because these algorithms shar…

Automatic Generation of Explicit Quadratic Programming Solvers
Maximilian Schaller, Daniel Arnstr\"om, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.11513

Automatic Generation of Explicit Quadratic Programming Solvers
We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a so…

High Probability Convergence of Distributed Clipped Stochastic Gradient Descent with Heavy-tailed Noise
Yuchen Yang, Kaihong Lu, Long Wang
https://arxiv.org/abs/2506.11647

High Probability Convergence of Distributed Clipped Stochastic Gradient Descent with Heavy-tailed Noise
In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this problem, a distributed clipped stochastic gradient descent algorithm is proposed, and the high probability convergence of the algorithm is studied. Existing works on distributed algorithms involving stochastic gradients only consider the light-tailed noises. Di…

Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters
Mathukumalli Vidyasagar
https://arxiv.org/abs/2506.11904 https://…

Convergence of Momentum-Based Optimization Algorithms with Time-Varying Parameters
In this paper, we present a unified algorithm for stochastic optimization that makes use of a "momentum" term; in other words, the stochastic gradient depends not only on the current true gradient of the objective function, but also on the true gradient at the previous iteration. Our formulation includes the Stochastic Heavy Ball (SHB) and the Stochastic Nesterov Accelerated Gradient (SNAG) algorithms as special cases. In addition, in our formulation, the momentum term is allowed to vary as a f…

This https://arxiv.org/abs/2405.08485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Doubly relaxed forward-Douglas--Rachford splitting for the sum of two nonconvex and a DC function
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class covers several important structures in the literature including the sum of three functions and the general DC program. We propose a splitting algorithm and prove the subsequential convergence to a stationary point of the problem. The full sequential convergenc…

Set Smoothness Unlocks Clarke Hyper-stationarity in Bilevel Optimization
He Chen, Jiajin Li, Anthony Man-cho So
https://arxiv.org/abs/2506.04587 https://…

Set Smoothness Unlocks Clarke Hyper-stationarity in Bilevel Optimization
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common alternative is to compute a hyper-stationary point -- a stationary point of the hyper-objective function formed by minimizing/maximizing the upper-level function over the lower-level solution set. However, existing approaches either yield weak notions of stationarity or rely on restrictive assumptions to ensure the smoothness of hyper-objective functions. In this paper, we remove these impractica…

A Model-Free Extremum Seeking Controller with Application to Tracking a Nonlinear Chemical Reaction
Alexander Zuyev, Victoria Grushkovska
https://arxiv.org/abs/2507.07749

A Model-Free Extremum Seeking Controller with Application to Tracking a Nonlinear Chemical Reaction
In this paper, we develop the extremum-seeking approach to generate admissible trajectories in a neighborhood of a given reference curve in the state space. The cost function of the problem represents the distance between the current system state and the reference curve, which is parameterized as a function of time. Such reference curves naturally arise as optimal trajectories in isoperimetric optimization problems for nonlinear chemical reactions, where the objective is to maximize the average…

A linesearch-based derivative-free method for noisy black-box problems
Alberto De Santis, Giampaolo Liuzzi, Stefano Lucidi
https://arxiv.org/abs/2508.00495 https://

A linesearch-based derivative-free method for noisy black-box problems
In this work we consider unconstrained optimization problems. The objective function is known through a zeroth order stochastic oracle that gives an estimate of the true objective function. To solve these problems, we propose a derivative-free algorithm based on extrapolation techniques. Under reasonable assumptions we are able to prove convergence properties for the proposed algorithms. Furthermore, we also give a worst-case complexity result stating that the total number of iterations where t…

This https://arxiv.org/abs/2403.06708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tikhonov Regularization for Stochastic Non-Smooth Convex Optimization in Hilbert Spaces
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one being differentiable and the other potentially non-smooth. We then use stochastic differential inclusions where the drift term is minus the subgradient of the objective function, and the diffusion term is either bounded or square-integrable. In this context, un…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
Xi Chen, Jinyan Fan
https://arxiv.org/abs/2507.05623 h…

A derivative-free regularization algorithm for equality constrained nonlinear least squares problems
In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via orthogonal spherical smoothing and propose a derivative-free regularization algorithm for solving the problem. At each iteration, a regularized augmented Lagrangian subproblem is solved to obtain a Newton-like step. If a sufficient decrease in the merit function of…

Projected Gradient Descent for Constrained Decision-Dependent Optimization
Zifan Wang, Changxin Liu, Thomas Parisini, Michael M. Zavlanos, Karl H. Johansson
https://arxiv.org/abs/2508.08856

Projected Gradient Descent for Constrained Decision-Dependent Optimization
This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explic…

Almost Sure Convergence for the Last Iterate of Stochastic Gradient Descent Schemes
Marcel Hudiani
https://arxiv.org/abs/2507.07281 https://

Almost Sure Convergence for the Last Iterate of Stochastic Gradient Descent Schemes
We study the almost sure convergence rate for the last iterate of stochastic gradient descent (SGD) and stochastic heavy ball (SHB) in the parametric setting when the objective function $F$ is globally convex or non-convex whose gradient is $γ$-Hölder. Using only discrete Gronwall's inequality without Robbins-Siegmund theorem nor martingale convergence theory, we recover results for both SGD and SHB: $\min_{s\leq t} \|\nabla F(w_s)\|^2 = o(t^{p-1})$ for non-convex objectives and $F(…

A Generalized Analytical Framework for the Nonlinear Best-Worst Method
Harshit M. Ratandhara, Mohit Kumar
https://arxiv.org/abs/2508.06048 https://arxiv.or…

A Generalized Analytical Framework for the Nonlinear Best-Worst Method
To eliminate the need for optimization software in calculating weights using the nonlinear model of the Best-Worst Method (BWM), Wu et al. proposed an analytical framework for deriving optimal interval-weights. They also introduced a secondary objective function to select the best optimal weight set. However, their framework is only compatible with a single Decision-Maker (DM) and preferences quantified using the Saaty scale. In this research, we generalize their framework to accommodate any nu…

A Cubic Regularization Method for Multiobjective Optimization
Douglas S. Gon\c{c}alves, Max L. N. Gon\c{c}alves, Jefferson G. Melo
https://arxiv.org/abs/2506.08181

A Cubic Regularization Method for Multiobjective Optimization
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective function is minimized. This model allows approximations for the first- and second-order derivatives, which must satisfy suitable error conditions. One interesting feature of the proposed algorithm is that the regularization parameter of the model and the accura…

Combinatorial Algorithm for Tropical Linearly Factorized Programming
Yuki Nishida
https://arxiv.org/abs/2507.07596 https://arxiv.org/…

Combinatorial Algorithm for Tropical Linearly Factorized Programming
The tropical semiring is a set of numbers $\mathbb{R}\cup\{-\infty\}$ with addition $a\oplus b:=\max(a,b)$ and multiplication $a\otimes b:=a+b$. As well as in conventional algebra, linear programming problem in the tropical semiring has been developed. In this study, we introduce a new type of tropical optimization problem, namely, tropical linearly factorized programming problem. This problem involves minimizing the objective function given by the product of tropical linear forms $c_{k,1}\otim…

This https://arxiv.org/abs/2404.17386 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Bregman Subgradient Methods for Nonsmooth Nonconvex Optimization Problems
This paper focuses on the problem of minimizing a locally Lipschitz continuous function. Motivated by the effectiveness of Bregman gradient methods in training nonsmooth deep neural networks and the recent progress in stochastic subgradient methods for nonsmooth nonconvex optimization problems \cite{bolte2021conservative,bolte2022subgradient,xiao2023adam}, we investigate the long-term behavior of stochastic Bregman subgradient methods in such context, especially when the objective function lack…

On Relatively Smooth Optimization over Riemannian Manifolds
Chang He, Jiaxiang Li, Bo Jiang, Shiqian Ma, Shuzhong Zhang
https://arxiv.org/abs/2508.03048 https://

On Relatively Smooth Optimization over Riemannian Manifolds
We study optimization over Riemannian embedded submanifolds, where the objective function is relatively smooth in the ambient Euclidean space. Such problems have broad applications but are still largely unexplored. We introduce two Riemannian first-order methods, namely the retraction-based and projection-based Riemannian Bregman gradient methods, by incorporating the Bregman distance into the update steps. The retraction-based method can handle nonsmooth optimization; at each iteration, the up…

This https://arxiv.org/abs/2410.14899 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Out-of-distribution Robust Optimization
In this paper, we consider the contextual robust optimization problem under an out-of-distribution setting. The contextual robust optimization problem considers a risk-sensitive objective function for an optimization problem with the presence of a context vector (also known as covariates or side information) capturing related information. While the existing works mainly consider the in-distribution setting, and the resultant robustness achieved is in an out-of-sample sense, our paper studies an…

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Oliver G. S. Lundqvist, Fabricio Oliveira
https://arxiv.org/abs/2506.04742

Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepON…

A Parameter-free Decentralized Algorithm for Composite Convex Optimization
Xiaokai Chen, Ilya Kuruzov, Gesualdo Scutari, Alexander Gasnikov
https://arxiv.org/abs/2508.01466 http…

A Parameter-free Decentralized Algorithm for Composite Convex Optimization
The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We propose a decentralized algorithm wherein agents ${\it adaptively}$ adjust their stepsize using local backtracking procedures that require ${\it no}$ ${\it global}$ (network) information or extensive inter-agent communications. Our adaptive decentralized method …

This https://arxiv.org/abs/2407.04562 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An SDE Perspective on Stochastic Inertial Gradient Dynamics with Time-Dependent Viscosity and Geometric Damping
Our approach is part of the close link between continuous dissipative dynamical systems and optimization algorithms. We aim to solve convex minimization problems by means of stochastic inertial differential equations which are driven by the gradient of the objective function. This will provide a general mathematical framework for analyzing fast optimization algorithms with stochastic gradient input. Our study is a natural extension of our previous work devoted to the first-order in time stochas…

Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
Leilei Cui, Zhong-Ping Jiang, Eduardo D. Sontag, Richard D. Braatz
https://arxiv.org/abs/2507.02131

Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
This article investigates the robustness of gradient descent algorithms under perturbations. The concept of small-disturbance input-to-state stability (ISS) for discrete-time nonlinear dynamical systems is introduced, along with its Lyapunov characterization. The conventional linear Polyak-Lojasiewicz (PL) condition is then extended to a nonlinear version, and it is shown that the gradient descent algorithm is small-disturbance ISS provided the objective function satisfies the generalized nonli…

Convergence Rate Analysis for Monotone Accelerated Proximal Gradient Method
Zepeng Wang, Juan Peypouquet
https://arxiv.org/abs/2507.00939 https://

Convergence Rate Analysis for Monotone Accelerated Proximal Gradient Method
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the objective function is strongly convex, without knowledge of the strong convexity parameter. This is the fastest convergence rate known for this algorithm.

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
Qiujiang Jin, Aryan Mokhtari
https://arxiv.org/abs/2507.00361 ht…

Affine-Invariant Global Non-Asymptotic Convergence Analysis of BFGS under Self-Concordance
In this paper, we establish global non-asymptotic convergence guarantees for the BFGS quasi-Newton method without requiring strong convexity or the Lipschitz continuity of the gradient or Hessian. Instead, we consider the setting where the objective function is strictly convex and strongly self-concordant. For an arbitrary initial point and any arbitrary positive-definite initial Hessian approximation, we prove global linear and superlinear convergence guarantees for BFGS when the step size is …