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The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Guo-Rong Wu , Chuan-Xi Zhu

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Optimization and Control · Mathematics 2011-07-01 Qihang Lin , Xi Chen , Javier Pena

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Optimization and Control · Mathematics 2026-05-04 Leandro Farias Maia , David H. Gutman , Renato D. C. Monteiro , Gilson N. Silva

We consider minimizing the sum of three convex functions, where the first one F is smooth, the second one is nonsmooth and proximable and the third one is the composition of a nonsmooth proximable function with a linear operator L. This…

Optimization and Control · Mathematics 2022-07-27 Adil Salim , Laurent Condat , Konstantin Mishchenko , Peter Richtárik

We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…

Numerical Analysis · Mathematics 2017-04-11 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato , Simone Rebegoldi

This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…

Optimization and Control · Mathematics 2026-01-12 Dimitris Boskos , Jorge Cortés , Sonia Martínez

We consider the problem of minimizing the sum of three convex functions: i) a smooth function $f$ in the form of an expectation or a finite average, ii) a non-smooth function $g$ in the form of a finite average of proximable functions…

Optimization and Control · Mathematics 2022-03-25 Konstantin Mishchenko , Peter Richtárik

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…

Optimization and Control · Mathematics 2015-10-27 Guanghui Lan

We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…

Optimization and Control · Mathematics 2018-12-04 Zhize Li , Jian Li

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 develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…

Optimization and Control · Mathematics 2019-12-13 Konstantin Mishchenko , Franck Iutzeler , Jérôme Malick

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Optimization and Control · Mathematics 2018-01-19 Bo Jiang , Tianyi Lin , Shiqian Ma , Shuzhong Zhang

In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…

Optimization and Control · Mathematics 2025-11-03 Xian-Jun Long , Kang Zeng , Gao-Xi Li , Minh N. Dao , Zai-Yun Peng

In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…

Systems and Control · Computer Science 2016-06-27 Ivano Notarnicola , Giuseppe Notarstefano

In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…

Optimization and Control · Mathematics 2016-10-28 Jingwei Liang , Jalal Fadili , Gabriel Peyré

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

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

Optimization and Control · Mathematics 2025-05-20 Laurent Condat , Elnur Gasanov , Peter Richtárik

The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…

Optimization and Control · Mathematics 2022-10-11 Xia Jiang , Xianlin Zeng , Jian Sun , Jie Chen , Lihua Xie

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

Optimization and Control · Mathematics 2021-02-02 Zhi Li , Wei Shi , Ming Yan

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

Optimization and Control · Mathematics 2019-01-28 Fred Moolekamp , Peter Melchior