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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…

Optimization and Control · Mathematics 2025-06-02 Kuangyu Ding , Kim-Chuan Toh

We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…

Numerical Analysis · Mathematics 2018-08-01 Anne Wald

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the…

Optimization and Control · Mathematics 2024-04-12 L. F. Prudente , D. R. Souza

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of…

Optimization and Control · Mathematics 2023-06-30 Francisco J. Aragón-Artacho , Pedro Pérez-Aros , David Torregrosa-Belén

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with…

Optimization and Control · Mathematics 2016-12-23 Nitish Shirish Keskar , Andreas Waechter

Optimizing strongly convex functions subject to linear constraints is a fundamental problem with numerous applications. In this work, we propose a block (accelerated) randomized Bregman-Kaczmarz method that only uses a block of constraints…

Numerical Analysis · Mathematics 2024-04-04 Lionel Tondji , Ion Necoara , Dirk A. Lorenz

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily…

Optimization and Control · Mathematics 2026-02-19 Shota Takahashi , Sebastian Pokutta , Akiko Takeda

This paper introduces adaptive Bregman proximal gradient algorithms for solving convex composite minimization problems without relying on global relative smoothness or strong convexity assumptions. Building upon recent advances in adaptive…

Optimization and Control · Mathematics 2025-08-05 Hongjia Ou , Puya Latafat , Andreas Themelis

When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may…

Machine Learning · Computer Science 2018-06-07 Bo Dai , Albert Shaw , Lihong Li , Lin Xiao , Niao He , Zhen Liu , Jianshu Chen , Le Song

This paper is devoted to minimizing the sum of a smooth function and a nonsmooth $\ell_1$-regularized term. This problem as a special cases includes the $\ell_1$-regularized convex minimization problem in signal processing, compressive…

Optimization and Control · Mathematics 2017-10-23 Yunhai Xiao , Soon-Yi Wu , Liqun Qi

We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…

Optimization and Control · Mathematics 2018-08-15 Quoc Tran-Dinh , Ahmet Alacaoglu , Olivier Fercoq , Volkan Cevher

Nonconvex-nonconcave minimax optimization has gained widespread interest over the last decade. However, most existing works focus on variants of gradient descent-ascent (GDA) algorithms, which are only applicable to smooth nonconvex-concave…

Optimization and Control · Mathematics 2025-01-17 Jiajin Li , Linglingzhi Zhu , Anthony Man-Cho So

In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient,…

Optimization and Control · Mathematics 2024-01-05 Qingsong Wang , Zehui Liu , Chunfeng Cui , Deren Han

In this paper, we provide a simple convergence analysis of proximal gradient algorithm with Bregman distance, which provides a tighter bound than existing result. In particular, for the problem of minimizing a class of convex objective…

Optimization and Control · Mathematics 2017-12-19 Yi Zhou , Yingbin Liang , Lixin Shen

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

Optimization and Control · Mathematics 2022-09-27 Shota Takahashi , Mituhiro Fukuda , Mirai Tanaka

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…

Optimization and Control · Mathematics 2017-06-20 Quang Van Nguyen , Olivier Fercoq , Volkan Cevher

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

Optimization and Control · Mathematics 2025-03-04 Lahcen El Bourkhissi , Ion Necoara , Panagiotis Patrinos , Quoc Tran-Dinh

Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…

Optimization and Control · Mathematics 2021-12-20 Yiyuan She , Zhifeng Wang , Jiuwu Jin

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

Optimization and Control · Mathematics 2023-04-11 Morteza Maleknia , Majid Soleimani-damaneh

In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized DC (Difference-of-Convex functions) programming, which is minimizing the sum of two separable DC parts and one…

Optimization and Control · Mathematics 2023-08-07 Hongjin He , Zhiyuan Zhang