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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

Optimization and Control · Mathematics 2013-02-14 Ion Necoara , Andrei Patrascu

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Optimization and Control · Mathematics 2020-03-10 Ion Necoara

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 study unconstrained optimization problems of nonsmooth, nonconvex Lipschitz functions, using only noisy pairwise comparisons governed by a known link function. Our goal is to compute a $(\delta,\varepsilon)$-Goldstein stationary point.…

Optimization and Control · Mathematics 2026-02-10 Taha El Bakkali , El Mahdi Chayti , Omar Saadi

In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…

Optimization and Control · Mathematics 2025-12-11 Spyridon Pougkakiotis , Dionysis Kalogerias

We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…

Optimization and Control · Mathematics 2018-12-19 Damek Davis , Dmitriy Drusvyatskiy

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Optimization and Control · Mathematics 2016-05-24 Sashank J. Reddi , Suvrit Sra , Barnabas Poczos , Alex Smola

Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…

Optimization and Control · Mathematics 2025-10-08 Zilong Ye , Shiqian Ma , Junfeng Yang , Danqing Zhou

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions---a wide class of functions which includes the additive and convex composite classes. At a…

Optimization and Control · Mathematics 2018-09-19 Damek Davis , Benjamin Grimmer

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Optimization and Control · Mathematics 2018-09-25 John Duchi , Feng Ruan

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

Optimization and Control · Mathematics 2025-11-19 Vitaliano S. Amaral , Marcio Antônio de A. Bortoloti , Jurandir O. Lopes , Gilson N. Silva

This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…

Optimization and Control · Mathematics 2016-05-02 Masoud Ahookhosh

This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…

Optimization and Control · Mathematics 2023-11-29 Pham Duy Khanh , Boris S. Mordukhovich , Dat Ba Tran

This paper considers decentralized nonsmooth nonconvex optimization problem with Lipschitz continuous local functions. We propose an efficient stochastic first-order method with client sampling, achieving the $(\delta,\epsilon)$-Goldstein…

Optimization and Control · Mathematics 2026-01-28 Xinyan Chen , Weiguo Gao , Luo Luo

In this paper, we study stochastic optimization of two-level composition of functions without Lipschitz continuous gradient. The smoothness property is generalized by the notion of relative smoothness which provokes the Bregman gradient…

Optimization and Control · Mathematics 2023-02-24 Yin Liu , Sam Davanloo Tajbakhsh

The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The…

Optimization and Control · Mathematics 2023-08-03 I. M. Prudnikov

This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…

Optimization and Control · Mathematics 2017-05-09 Shu Liang , Xianlin Zeng , Yiguang Hong

In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…

Optimization and Control · Mathematics 2024-12-03 Ion Necoara , Nitesh Kumar Singh

This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the…

Optimization and Control · Mathematics 2024-11-07 Wenzhi Gao , Qi Deng

We study the problem of minimizing a strongly convex, smooth function when we have noisy estimates of its gradient. We propose a novel multistage accelerated algorithm that is universally optimal in the sense that it achieves the optimal…

Optimization and Control · Mathematics 2019-10-29 Necdet Serhat Aybat , Alireza Fallah , Mert Gurbuzbalaban , Asuman Ozdaglar