Tootfinder

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…

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…

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…

Tikhonov regularized second-order dynamical systems with Hessian-driven damping for solving convex optimization problems
Xiangkai Sun, Guoxiang Tian, Huan Zhang
https://arxiv.org/abs/2506.15968

Tikhonov regularized second-order dynamical systems with Hessian-driven damping for solving convex optimization problems
This paper deals with a Tikhonov regularized second-order dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate setting of the parameters, we first obtain fast convergence results of the function value along the trajectory generated by the dynamical system. Then, we show that the trajectory generated by the dynamical system converges weakly to a minimizer of the convex optimization…

The $\sigma_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond
Jonah A. J. Duncan, Luc Nguyen
https://arxiv.org/abs/2507.16394

The $σ_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond
Let $(M^n,g_0)$ be a smooth compact Riemannian manifold of dimension $n\geq 3$ with smooth non-empty boundary $\partial M$. Let $Γ\subset\mathbb{R}^n$ be a symmetric convex cone and $f$ a symmetric defining function for $Γ$ satisfying standard assumptions. Denoting by $A_{g_u}$ the Schouten tensor of a conformal metric $g_u = u^{-2}g_0$, we show that the associated fully nonlinear Loewner-Nirenberg problem \begin{align*} \begin{cases} f(λ(-g_u^{-1}A_{g_u})) = \frac{1}{2}, \quad λ(-g_u…

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…

Understanding Data Influence with Differential Approximation
Haoru Tan, Sitong Wu, Xiuzhe Wu, Wang Wang, Bo Zhao, Zeke Xie, Gui-Song Xia, Xiaojuan Qi
https://arxiv.org/abs/2508.14648

Understanding Data Influence with Differential Approximation
Data plays a pivotal role in the groundbreaking advancements in artificial intelligence. The quantitative analysis of data significantly contributes to model training, enhancing both the efficiency and quality of data utilization. However, existing data analysis tools often lag in accuracy. For instance, many of these tools even assume that the loss function of neural networks is convex. These limitations make it challenging to implement current methods effectively. In this paper, we introduce …

The Gaussian Minkowski problem for epigraphs of convex functions
Xiao Li, Deping Ye
https://arxiv.org/abs/2508.12028 https://arxiv.org/pdf/2508.12028

The Gaussian Minkowski problem for epigraphs of convex functions
A variational formula is derived by combining the Gaussian volume of the epigraph of a convex function $φ$ and the perturbation of $φ$ via the infimal convolution. This formula naturally leads to a Borel measure on $\mathbb{R}^n$ and a Borel measure on the unit sphere $S^{n-1}$. The resulting Borel measure on $\mathbb{R}^n$ will be called the Euclidean Gaussian moment measure of the convex function $φ$, and the related Minkowski-type problem will be studied. In particular, the newly posed Mi…

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…

Outer symplectic billiard map at infinity
Peter Albers, Ana Chavez Caliz, Serge Tabachnikov
https://arxiv.org/abs/2508.15142 https://arxiv.org/pdf/2508.151…

Outer symplectic billiard map at infinity
We show that the second iteration $T^2$ of the outer symplectic billiard map with respect to a convex domain $M$ in a symplectic vector space is approximated by an explicit Hamiltonian flow for points far away from $M$. More precisely, denote by $N$ the symplectic polar dual of the symmetrization $M\ominus M$ of $M$. If we write $N$ as the unit level set of a 1-homogeneous function $H$, then the difference between $T^2$ and the time-2-Hamiltonian flow of $H$ applied to a point $x$ is smaller …

On Steiner entire function
Maria Dospolova, Mikhail Germanskov, Dmitry Zaporozhets
https://arxiv.org/abs/2507.11626 https://arxiv.org…

On Steiner entire function
We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and encodes key geometric information about the set. We establish fundamental results on its order, type, and canonical product representation, and show how its analytic growth properties characterize Gaussian continuity. In particular, we provide new criteria for th…

Quantum Algorithms for Projection-Free Sparse Convex Optimization
Jianhao He, John C. S. Lui
https://arxiv.org/abs/2507.08543 https://

Quantum Algorithms for Projection-Free Sparse Convex Optimization
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain $\mathcal{D} \subset \mathbb{R}^d$, we propose two quantum algorithms for sparse constraints that finds a $\varepsilon$-optimal solution with the query complexity of $O(\sqrt{d}/\varepsilon)$ and $O(1/\varepsilon)$ by using the function value oracle, reducing a fa…

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…

Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties
Lasse Leskel\"a, Ian V\"alimaa
https://arxiv.org/abs/2508.12103

Sub-Poisson distributions: Concentration inequalities, optimal variance proxies, and closure properties
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance parameter in the sub-Gaussian setting. This framework allows us to derive a Bennett-type concentration inequality without boundedness assumptions and to show that the sub-Poisson property is closed under key operations including independent sums and convex com…

Global well-posedness for the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions
Taiki Takeuchi, Keiichi Watanabe
https://arxiv.org/abs/2507.13684

Global well-posedness for the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions
In this paper, we consider the Keller--Segel--Navier--Stokes system with nonlinear boundary conditions in a bounded smooth (and not necessarily convex) domain $Ω\subset \mathbb{R}^N$, $N \ge 2$, where the chemotactic sensitivity $S$ is assumed to have values in $\mathbb{R}^{N \times N}$ which accounts for rotational fluxes. In contrast to the case where $S$ is a scalar-valued function (or $S$ is the identity matrix), in our system, the normal derivative for the density $n$ of the cell is given…

A convexity-type functional inequality with infinite convex combinations
Matyas Barczy, Zsolt P\'ales
https://arxiv.org/abs/2508.02474 https://arxiv.or…

A convexity-type functional inequality with infinite convex combinations
Given a function $f$ defined on a nonempty and convex subset of the $d$-dimensional Euclidean space, we prove that if $f$ is bounded from below and it satisfies a convexity-type functional inequality with infinite convex combinations, then $f$ has to be convex. We also give alternative proofs of a generalization of some known results on convexity with infinite convex combinations due to Daróczy and Páles (1987) and Pavić (2019) using a probabilistic version of Jensen inequality.

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Guillaume Garrigos, Daniel Cortild, Lucas Ketels, Juan Peypouquet
https://arxiv.org/abs/2507.14122

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate of SGD in this context. Recent advances suggest that it should be possible. For instance, it can be achieved by making the additional, yet unverifiable, assumption that the variance of the stochastic gradients is uniformly bounded. In this paper, we show that …

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…

Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
Fabian Mussnig, Jacopo Ulivelli
https://arxiv.org/abs/2508.11600 https://

Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries
An explicit solution to the Christoffel-Minkowski problem for convex bodies of revolution is presented. The conditions on the prescribed measure involve only first moments over spherical caps, and the support function of the resulting convex body is given by an explicit representation formula in terms of the measure. More generally, existence problems for mixed area measures are addressed. The approach relies on constructing explicit convex solutions to mixed Monge-Ampère equations on $\mathbb…

Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables
Hamza Hanbali, Jan Dhaene, Daniel Linders
https://arxiv.org/abs/2508.12606 ht…

Dependence bounds for the difference of stop-loss payoffs on the difference of two random variables
This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used to construct upper and lower bounds for the expected payoff, despite the fact that the payoff function is neither convex nor concave. The answer to the central question of the paper requires studying the crossing points of the cdf of the original difference …

Enumeration of Hopf Monoids and Supersolvable Convex Geometries
Yichen Ma
https://arxiv.org/abs/2506.00380 https://arxiv.org/pdf/2506…

Enumeration of Hopf Monoids and Supersolvable Convex Geometries
We consider the Hopf monoid of convex geometries, which contains partial orders as a Hopf submonoid, and investigate combinatorial invariants constructed from canonical characters on them. Each invariant consists of a pair: a polynomial and a more general quasisymmetric function. We provide combinatorial descriptions of the polynomial invariants and prove combinatorial reciprocity theorems for polynomials that generalize order and enriched order polynomials within a unified framework. For the q…

Generalized convexity and quantitative estimates for constant mean curvature spacelike hypersurfaces in Anti-de Sitter space
Enrico Trebeschi
https://arxiv.org/abs/2508.05349 ht…

Generalized convexity and quantitative estimates for constant mean curvature spacelike hypersurfaces in Anti-de Sitter space
We study the principal curvatures of properly embedded constant mean curvature hypersurfaces in the Anti-de Sitter space $\mathbb{H}^{n,1}$. We generalize the notion of convex hull and give an upper bound on the principal curvatures which only depends on the width of the $H-$shifted convex hull. This analysis has two direct consequences. First, it allows to bound the sectional curvature of $H-$hypersurfaces by an explicit function of the the width of the $H-$shifted convex hull. Second, we boun…

Inverse design of the transmission matrix in a random system using Reinforcement Learning
Yuhao Kang
https://arxiv.org/abs/2506.13057 https://

Inverse design of the transmission matrix in a random system using Reinforcement Learning
This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object function to achieve three types of transmission matrices: (1) Fixed-ratio power conversion and zero-transmission mode in rank-1 matrices, (2) exceptional points with degenerate eigenvalues and unidirectional mode conversion, and (3) uniform channel participat…

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 …

Adaptive determinantal scheduling with fairness in wireless networks
H. P. Keeler, B. B{\l}aszczyszyn
https://arxiv.org/abs/2506.11738 https://

Adaptive determinantal scheduling with fairness in wireless networks
We propose a novel framework for wireless network scheduling with fairness using determinantal (point) processes. Our approach incorporates the repulsive nature of determinantal processes, generalizing traditional Aloha protocols that schedule transmissions independently. We formulate the scheduling problem with an utility function representing fairness. We then recast this formulation as a convex optimization problem over a certain class of determinantal point processes called $L$-ensembles, w…

Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
Jes\'us Due\~nas, Carmen N\'u\~nez, Rafael Obaya
https://arxiv.org/abs/2507.00545

Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
The long-term dynamics of a Bonifacio-Lugiato model of optical superfluorescence is investigated. The scalar ordinary differential equation modelling the phenomenon is given by a concave-convex autonomous function of the state variable that is excited by a time-dependent input, $I(t)$. The system's response is described in terms of the dynamical characteristics of the input function, with particular focus on uniform stability or bistability cases. Building on previous published results, the ope…

Asymptotic convexity of wide and shallow neural networks
Vivek Borkar, Parthe Pandit
https://arxiv.org/abs/2507.01044 https://arxiv.o…

Asymptotic convexity of wide and shallow neural networks
For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible explanation of their observed good performance.

Always-convex harmonic shears
Rodrigo Hern\'andez, Mar\'ia J. Mart\'in, Fernando P\'erez-Gonz\'alez, Magdalena Wo{\l}oszkiewicz-Cyll
https://arxiv.org/abs/2507.01592

Always-convex harmonic shears
We determine completely the analytic functions $φ$ in the unit disk $\mathbb D$ such that for all (normalized) orientation-preserving harmonic mappings $f=h+\overline g$ which satisfy $h+ g=φ$, the condition that $f$ maps $\mathbb D$ onto a convex domain holds. As a consequence, we obtain the following more general result: for a given complex number $η$, with $|η|=1$, we characterize those holomorphic mappings $φ$ in $\mathbb D$ such that every harmonic function $f=h+\overline g$…

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…

Polyconvex double well functions
Didier Henrion (LAAS-POP), Martin Kru\v{z}\'ik (UTIA / CAS)
https://arxiv.org/abs/2508.14541 https://arxiv.org/pdf/250…

Polyconvex double well functions
We investigate polyconvexity of the double well function $f(X)\,:= |X-X_1|^2|X-X_2|^2$ for given matrices $X_1, X_2 \in R^{n \times n}$. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. We prove that $f$ is polyconvex if and only if the singular values of the matrix difference $X_1 - X_2$ are all equal. This condition allows the function to be decomposed…

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…

This https://arxiv.org/abs/2301.10980 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Beyond scalar quasi-arithmetic means: Quasi-arithmetic averages and quasi-arithmetic mixtures in information geometry
We generalize quasi-arithmetic means beyond scalars by considering the gradient map of a Legendre type real-valued function. The gradient map of a Legendre type function is proven strictly comonotone with a global inverse. It thus yields a generalization of strictly mononotone and differentiable functions generating scalar quasi-arithmetic means. Furthermore, the Legendre transformation gives rise to pairs of dual quasi-arithmetic averages via the convex duality. We study the invariance and equ…

Essential norm and Schatten class of Hankel operators between weighted Fock spaces
Yi Liu, Yufeng Lu
https://arxiv.org/abs/2508.11882 https://arxiv.org/pdf…

Essential norm and Schatten class of Hankel operators between weighted Fock spaces
In this paper, we characterize the essential norm of Hankel operators from a weighted Fock space $F_φ^{p}$ to a weighted Lebesgue space $L_φ^{q}$ for all $1 \leq p, q < \infty$. Additionally, we characterize the Schatten-$h$ class membership for Hankel operators acting from $F_φ^{2}$ to $L_φ^{2}$, where the class is defined by a continuous increasing convex function $h$.

The convex structure of the Parisi formula for multi-species spin glasses
Hong-Bin Chen, Victor Issa, Jean-Christophe Mourrat
https://arxiv.org/abs/2508.06397 https://

The convex structure of the Parisi formula for multi-species spin glasses
We study the free energy of mean-field multi-species spin glasses with convex covariance function. For such models with $D$ species, the Parisi formula is known to be valid, and expresses the limit free energy as a supremum over monotone probability measures on $\mathbb{R}_+^D$. We show here that one can transform this representation into a supremum over all probability measures on $\mathbb{R}_+^D$ of a concave functional. We then deduce that the Parisi formula admits a unique maximizer. Using …

Adapted Renormalized Volume for Hyperbolic 3-Manifolds with Compressible Boundary
Viola Giovannini
https://arxiv.org/abs/2507.19291 https://arxiv.org/pdf/2…

Adapted Renormalized Volume for Hyperbolic 3-Manifolds with Compressible Boundary
The renormalized volume is a smooth function associating to every convex co-compact hyperbolic $3$-manifold $M$ a real number. When the boundary of $M$ is incompressible, the renormalized volume is always positive, otherwise there are sequences of convex co-compact structures on $M$ whose renormalized volumes diverge to minus infinity. We define here a new version of the renormalized volume which adapts to the compressible boundary case, satisfying properties analogous to those of the classic…

PDE-Constrained High-Order Mesh Optimization
Tzanio Kolev, Boyan Lazarov, Ketan Mittal, Mathias Schmidt, Vladimir Tomov
https://arxiv.org/abs/2507.01917 ht…

PDE-Constrained High-Order Mesh Optimization
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regula…

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…

Replaced article(s) found for math.GM. https://arxiv.org/list/math.GM/new
[1/1]:
- Zeta function for convex domains
Nikita Kalinin
https://

Characterization of Hilbertizable spaces via convex functions
Nicolas Borchard, Gerd Wachsmuth
https://arxiv.org/abs/2506.04686 https://

Characterization of Hilbertizable spaces via convex functions
We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space.

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

This https://arxiv.org/abs/2309.09432 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Entire solutions of two-convex Lagrangian mean curvature flows
Given an entire $C^2$ function $u$ on $\mathbb{R}^n$, we consider the graph of $D u$ as a Lagrangian submanifold of $\mathbb{R}^{2n}$, and deform it by the mean curvature flow in $\mathbb{R}^{2n}$. This leads to the special Lagrangian evolution equation, a fully nonlinear Hessian type PDE. We prove long-time existence and convergence results under a 2-positivity assumption of $(I+(D^2 u)^2)^{-1}D^2 u$. Such results were previously known only under the stronger assumption of positivity of $D^2 u…

Set-Based Control Barrier Functions and Safety Filters
Kim P. Wabersich, Felix Berkel, Felix Gruber, Sven Reimann
https://arxiv.org/abs/2507.07805 https://…

Set-Based Control Barrier Functions and Safety Filters
High performance and formal safety guarantees are common requirements for industrial control applications. Control barrier function (CBF) methods provide a systematic approach to the modularization of safety and performance. However, the design of such CBFs can be challenging, which limits their applicability to large-scale or data-driven systems. This paper introduces the concept of a set-based CBF for linear systems with convex constraints. By leveraging control invariant sets from reachabili…

Learning Parametric Convex Functions
Maximilian Schaller, Alberto Bemporad, Stephen Boyd
https://arxiv.org/abs/2506.04183 https://arx…

Learning Parametric Convex Functions
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex optimization family, in domain specific languages for convex optimization. In this paper we address the problem of fitting a parametrized convex function that is compatible with disciplined programming, to some given data. This allows us to fit a function arising i…

Signed Minkowski decompositions of convex polygons into minimum simplices and factorization of max-plus functions
Soujun Kitagawa
https://arxiv.org/abs/2506.20999

Signed Minkowski decompositions of convex polygons into minimum simplices and factorization of max-plus functions
Signed Minkowski decomposition is an expression of a polytope as a Minkowski sum and difference of smaller polytopes. Signed Minkowski decompositions of a polytope can be interpreted as factorizations of a max-plus (tropical) function. We review two relations about Minkowski decompositions, and we prove that any 2-dimensional integral polytopes (polygons) have a signed Minkowski decomposition which consists of integral points, integral line segments of length 1, and integral triangles of area 1…

$\mathbf{C^2}$-Lusin approximation of convex functions: one variable case
Pawe{\l} Goldstein, Piotr Haj{\l}asz
https://arxiv.org/abs/2505.22975 https://

$\mathbf{C^2}$-Lusin approximation of convex functions: one variable case
We prove that if $f:(a,b)\to\mathbb{R}$ is convex, then for any $\varepsilon>0$ there is a convex function $g\in C^2(a,b)$ such that $|\{f\neq g\}|<\varepsilon$ and $\Vert f-g\Vert_\infty<\varepsilon$.

Approximate transonic shock solution for hypersonic flow past a large curved convex wedge
Dian Hu
https://arxiv.org/abs/2508.03255 https://arxiv.org/pdf/25…

Approximate transonic shock solution for hypersonic flow past a large curved convex wedge
In this paper, we study the existence of a global transonic shock generated by hypersonic potential flow over a large curved convex wedge. Modeling 2-dimensional steady potential flow leads to a free boundary value problem of quasilinear equation. By applying the hodograph transformation, in which one of the coordinate is the unknown function, this problem is reduced to a free boundary value problem of linear equation. For hypersonic incoming flow with adiabatic index $γ=2$, we construct an ap…

The Optimal Smoothings of Sublinear Functions and Convex Cones
Thabo Samakhoana, Benjamin Grimmer
https://arxiv.org/abs/2508.06681 https://arxiv.org/pdf/25…

The Optimal Smoothings of Sublinear Functions and Convex Cones
This paper considers the problem of smoothing convex functions and sets, seeking the nearest smooth convex function or set to a given one. For convex cones and sublinear functions, a full characterization of the set of all optimal smoothings is given. These provide if and only if characterizations of the set of optimal smoothings for any target level of smoothness. Optimal smoothings restricting to either inner or outer approximations also follow from our theory. Finally, we apply our theory to…

Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps
Wentao Zhang, Baoyong Zhang, Deming Yuan, Shengyuan Xu, Vincent K. N. Lau
https://arxiv.org/abs/2508.09411

Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps
This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metrics, we propose a distributed online stochastic mirror descent convex-concave optimization algorithm with time-varying predictive mappings. Taking dynamic saddle point regret as a p…

Gradient regularity for widely degenerate elliptic partial differential equations
Michael Strunk
https://arxiv.org/abs/2506.11708 https://

Gradient regularity for widely degenerate elliptic partial differential equations
In this paper, we investigate the regularity of weak solutions $u\colonΩ\to\mathbb{R}$ to elliptic equations of the type \begin{equation*} \mathrm{div}\, \nabla \mathcal{F}(x,Du) = f\qquad\text{in $Ω$}, \end{equation*} whose ellipticity degenerates in a fixed bounded and convex set $E\subset\mathbb{R}^n$ with $0\in \mathrm{Int}\, E$. Here, $Ω\subset\mathbb{R}^n$ denotes a bounded domain, and $\mathcal{F} \colon Ω\times\mathbb{R}^n \to\mathbb{R}_{\geq 0}$ is a function with the properties:…

A Proximal Variable Smoothing for Minimization of Nonlinearly Composite Nonsmooth Function -- Maxmin Dispersion and MIMO Applications
Keita Kume, Isao Yamada
https://arxiv.org/abs/2506.05974

A Proximal Variable Smoothing for Minimization of Nonlinearly Composite Nonsmooth Function -- Maxmin Dispersion and MIMO Applications
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure inspired by a proximal gradient-type method. More precisely, the proposed algorithm consists of two steps: (i) a gradient descent of a time-varying smoothed surrogate function designed partially with the Moreau envelope of the weakly convex function; (ii) an appli…

Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo
Ruiyu Han, Gautam Iyer, Dejan Slep\v{c}ev
https://arxiv.org/abs/2508.02763 https://

Polynomial complexity sampling from multimodal distributions using Sequential Monte Carlo
We study a sequential Monte Carlo algorithm to sample from the Gibbs measure with a non-convex energy function at a low temperature. We use the practical and popular geometric annealing schedule, and use a Langevin diffusion at each temperature level. The Langevin diffusion only needs to run for a time that is long enough to ensure local mixing within energy valleys, which is much shorter than the time required for global mixing. Our main result shows convergence of Monte Carlo estimators with …

This https://arxiv.org/abs/2406.05694 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Low Rank Neural Representation of Entropy Solutions
We construct a new representation of entropy solutions to nonlinear scalar conservation laws with a smooth convex flux function in a single spatial dimension. The representation is a generalization of the method of characteristics and posseses a compositional form. While it is a nonlinear representation, the embedded dynamics of the solution in the time variable is linear. This representation is then discretized as a manifold of implicit neural representations where the feedforward neural netwo…

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…

Efficient Computation of Marton's Error Exponent via Constraint Decoupling
Jiachuan Ye, Shitong Wu, Lingyi Chen, Wenyi Zhang, Huihui Wu, Hao Wu
https://arxiv.org/abs/2507.19816

Efficient Computation of Marton's Error Exponent via Constraint Decoupling
The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation methods of the Marton's error exponent remain underdeveloped due to its formulation as a non-convex optimization problem with limited efficient solvers. While a recent grid search algorithm can compute its inverse function, it incurs prohibitive computational cos…

This https://arxiv.org/abs/2501.18584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Corks, exotic 4-manifolds and genus functions
We prove that every 4-dimensional oriented handlebody without 3- and 4-handles can be modified to admit infinitely many exotic smooth structures, and further that their genus functions are pairwise equivalent. We furthermore show that, for any 4-manifold admitting an embedding into a symplectic 4-manifold with weakly convex boundary, its genus function is algebraically realized as those of infinitely many pairwise exotic 4-manifolds. We also prove that, for any two 4-manifolds with non-degenera…

Bohr inequality and Bohr-Rogosinski inequality for $K$-Quasiconformal harmonic mappings
Molla Basir Ahamed, Taimur Rahman
https://arxiv.org/abs/2508.00012 https://

Bohr inequality and Bohr-Rogosinski inequality for $K$-Quasiconformal harmonic mappings
In this paper, we prove several sharp Bohr-type and Bohr-Rogosinski-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, whose analytic part is subordinate to a function belonging to the class of concave univalent functions on $\mathbb{D}$. In addition, we derive Bohr-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{D}$, where the analytic part is subordinate to a function from the Ma-Minda class of convex and star…

On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation
Souvik Ghosh, Kallol Paul, Debmalya Sain, Shamim Sohel
https://arxiv.org/abs/2508.04971

On some subspaces of vector-valued continuous function space, from the perspective of Best coapproximation
This article explores anti-coproximinal and strongly anti-coproximinal subspaces in the spaces of vector-valued continuous functions and operator spaces. We provide a complete characterization of strongly anti-coproximinal subspaces in $ C_0(K, \mathbb{X}) $, under the assumption that the unit ball of $ \mathbb{X}^* $ is the closed convex hull of its weak*-strongly exposed points. Additionally, the work includes a stability analysis of anti-coproximinal and strongly anti-coproximinal subspaces …

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited
Guillaume Boutoille, Gilles Pag\`es
https://arxiv.org/abs/2506.01746

Optimal Bregman quantization : existence and uniqueness of optimal quantizers revisited
In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which generates the divergence, espcially in the quadratic case ($r=2$). We then prove a uniqueness theorem ``à la Trushkin'' in one dimension for strongly unimodal distributions and divergences gerated by strictly convex functions whiose thire dervative is eithe…

An inexact variable metric proximal linearization method for composite optimization over embedded submanifolds
Hao He, Ruyu Liu, Yitian Qian, Shaohua Pan
https://arxiv.org/abs/2508.12003

An inexact variable metric proximal linearization method for composite optimization over embedded submanifolds
This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth problems, we propose an inexact variable metric proximal linearization method by leveraging its composite structure and the retraction and first-order information of $\mathcal{M}$, which at each iteration seeks an inexact solution to a subspace constrained strong…

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- Order isomorphisms of sup-stable function spaces: continuous, Lipschitz, c-convex, and beyond
Pierre-Cyril Aubin-Frankowski, St\'ephane Gaubert

Biobjective optimization with M-convex functions
Ellen H. Fukuda, Satoru Iwata, Itsuki Nakagawa
https://arxiv.org/abs/2507.23423 https://arxiv.org/pdf/2507…

Biobjective optimization with M-convex functions
In this paper, we deal with two ingredients that, as far as we know, have not been combined until now: multiobjective optimization and discrete convex analysis. First, we show that the entire Pareto optimal value set can be obtained in polynomial time for biobjective optimization problems with discrete convex functions, in particular, involving an M$^\natural$-convex function and a linear function with binary coefficients. We also observe that a more efficient algorithm can be obtained in the s…

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 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/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…

The matrix weighted real-analytic double fibration transforms
Hiroyuki Chihara, Shubham R. Jathar, Jesse Railo
https://arxiv.org/abs/2506.24067 https://

The matrix weighted real-analytic double fibration transforms
We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with …

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…

Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers
Vitali Pirau, Roland Hildebrand
https://arxiv.org/abs/2507.01812

Numerical analysis of the convex relaxation of the barrier parameter functional of self-concordant barriers
Self-concordant barriers are essential for interior-point algorithms in conic programming. To speed up the convergence it is of interest to find a barrier with the lowest possible parameter for a given cone. The barrier parameter is a non-convex function on the set of self-concordant barriers on a given cone, and finding an optimal barrier amounts to solving a non-convex infinite-dimensional optimization problem. In this work we study the degradation of the optimal value of the problem when the…

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
Markus Friedemann, Gerd Wachsmuth
https://arxiv.org/abs/2508.10692 https:…

A trust-region method for optimal control of ODEs with continuous-or-off controls and TV regularization
A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally a total variation regularization is applied to penalize switches. Our solution method combines a trust-region method and a proximal gradient method. The subproblems are solved via Bellman's optimality principle. Convergence with respect to a criticality measure is proven…

This https://arxiv.org/abs/2503.16398 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The global convergence time of stochastic gradient descent in non-convex landscapes: Sharp estimates via large deviations
In this paper, we examine the time it takes for stochastic gradient descent (SGD) to reach the global minimum of a general, non-convex loss function. We approach this question through the lens of randomly perturbed dynamical systems and large deviations theory, and we provide a tight characterization of the global convergence time of SGD via matching upper and lower bounds. These bounds are dominated by the most "costly" set of obstacles that the algorithm may need to overcome in order to reach…

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…

Fast convex optimization via inertial systems with asymptotic vanishing viscous and Hessian-driven damping
Zepeng Wang, Juan Peypouquet
https://arxiv.org/abs/2506.21730

Fast convex optimization via inertial systems with asymptotic vanishing viscous and Hessian-driven damping
We study the convergence rate of a family of inertial algorithms, which can be obtained by discretization of an inertial system combining asymptotic vanishing viscous and Hessian-driven damping. We establish a fast sublinear convergence rate in case the objective function is convex and satisfies Polyak-Łojasiewicz inequality. We also establish a linear convergence rate for smooth strongly convex functions. The results can provide more insights into the convergence property of Nesterov's accele…

This https://arxiv.org/abs/2409.10773 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tight Lower Bounds under Asymmetric High-Order Hölder Smoothness and Uniform Convexity
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order Hölder smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are Hölder continuous with degree $ν$ and parameter $H$, and that is uniformly convex with degree $q$ and parameter $σ$, we focus on two asymmetric cases: (1) $q > p + ν$, and (2) $q < p+ν$. Given up to $p^{th}$-order oracle access, we establish worst-case oracle complexities of $Ω\left(…

This https://arxiv.org/abs/2412.06436 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Adaptively Inexact Method for Bilevel Learning Using Primal-Dual Style Differentiation
We consider a bilevel learning framework for learning linear operators. In this framework, the learnable parameters are optimized via a loss function that also depends on the minimizer of a convex optimization problem (denoted lower-level problem). We utilize an iterative algorithm called `piggyback' to compute the gradient of the loss and minimizer of the lower-level problem. Given that the lower-level problem is solved numerically, the loss function and thus its gradient can only be computed …

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…

Parallel block coordinate descent methods with identification strategies
Rolando Lopes, Sandra A. Santos, Paulo J. S. Silva
https://arxiv.org/abs/2507.22277 https://

Parallel block coordinate descent methods with identification strategies
This work presents a parallel variant of the algorithm introduced in [Acceleration of block coordinate descent methods with identification strategies Comput. Optim. Appl. 72(3):609--640, 2019] to minimize the sum of a partially separable smooth convex function and a possibly non-smooth block-separable convex function under simple constraints. It achieves better efficiency by using a strategy to identify the nonzero coordinates that allows the computational effort to be focused on using a nonuni…

Mean-Field Langevin Diffusions with Density-dependent Temperature
Yu-Jui Huang, Zachariah Malik
https://arxiv.org/abs/2507.20958 https://arxiv.org/pdf/2507…

Mean-Field Langevin Diffusions with Density-dependent Temperature
In the context of non-convex optimization, we let the temperature of a Langevin diffusion to depend on the diffusion's own density function. The rationale is that the induced density reveals to some extent the landscape imposed by the non-convex function to be minimized, such that a density-dependent temperature can provide location-wise random perturbation that may better react to, for instance, the location and depth of local minimizers. As the Langevin dynamics is now self-regulated by its o…

Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality
Vo Si Trong Long, Nguyen Mau Nam, Len White
https://arxiv.org/abs/2507.07377

Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality
In this paper, we investigate general and generalized differentiation properties of theoptimal value function associated with perturbed optimization problems. We begin with a comprehensive analysis of its effective domain, epigraph, strict epigraph, convexity, near convexity, continuity, and Lipschitz-type behavior, in both convex and nonconvex settings. Next, we propose a duality framework for constrained optimization problems with set-valued constraints, based on the notion of the Fenchel con…

Composite Optimization with Indicator Functions: Stationary Duality and a Semismooth Newton Method
Penghe Zhang, Naihua Xiu, Houduo Qi
https://arxiv.org/abs/2506.08374

Composite Optimization with Indicator Functions: Stationary Duality and a Semismooth Newton Method
Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual problem is a more challenging topic that has not been well addressed. One possible reason is that the Fenchel conjugate of any indicator function is finite only at the origin. This work aims to explore the dual optimization for the sum of a strongly convex function…

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.

Discrete and Continuous Difference of Submodular Minimization
George Orfanides, Tim Hoheisel, Marwa El Halabi
https://arxiv.org/abs/2506.07952 https://

Discrete and Continuous Difference of Submodular Minimization
Submodular functions, defined on continuous or discrete domains, arise in numerous applications. We study the minimization of the difference of two submodular (DS) functions, over both domains, extending prior work restricted to set functions. We show that all functions on discrete domains and all smooth functions on continuous domains are DS. For discrete domains, we observe that DS minimization is equivalent to minimizing the difference of two convex (DC) functions, as in the set function cas…

This https://arxiv.org/abs/2503.14328 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Risk-Sensitive Model Predictive Control for Interaction-Aware Planning -- A Sequential Convexification Algorithm
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable convex upper bounds to both the objective function, and to frequently used penalty terms for collision avoidance, allowing us to efficiently solve the generally nonconvex optimal control problem as a sequence of convex problems. Simulations of a robot navigatin…

A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization
A. A. Vyguzov, F. S. Stonyakin
https://arxiv.org/abs/2507.05669

A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization
We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth and relatively strongly convex objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size based on both the relative smoothness constant and the Triangle Scaling Exponent (TSE) of the Bregman divergence. Our method does not require prior knowledge of the function parameters and guarantees convergence using only loc…

Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
Ying Hu, Guomin Liu, Shanjian Tang
https://arxiv.org/abs/2507.06118

Relationship between maximum principle and dynamic programming principle for recursive optimal control problem of stochastic evolution equations
This paper aims to study the relationship between the maximum principle and the dynamic programming principle for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and the value function may be nonsmooth. By making use of the notion of conditionally expected operator-valued backward stochastic integral equations, we establish a connection between the first and second-order adjoint processes in MP and the general derivatives o…

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…

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 …

Distributionally Robust Shape and Topology Optimization
Charles Dapogny, Julien Prando, Boris Thibert
https://arxiv.org/abs/2507.21574 https://arxiv.org/pd…

Distributionally Robust Shape and Topology Optimization
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the cost function of the design to be minimized depend on uncertain parameters. The probability distribution of the latter is itself known imperfectly, through a nominal law, reconstructed from a few observed samples. The distributionally robust optimal design pro…