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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

This note studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of different local objective…

Optimization and Control · Mathematics 2021-03-04 Xia Jiang , Xianlin Zeng , Jian Sun , Jie Chen

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

We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…

Optimization and Control · Mathematics 2024-03-01 Yiming Zhou , Wei Dai

In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by…

Optimization and Control · Mathematics 2018-10-25 Ehsan Kazemi , Liqiang Wang

In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle this problem we chose a continuous forward-backward approach and…

Optimization and Control · Mathematics 2020-01-29 Radu Ioan Bot , Laura Kanzler

We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…

Optimization and Control · Mathematics 2019-05-17 Radu Ioan Bot , Axel Böhm

The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…

Functional Analysis · Mathematics 2019-08-30 Fuying Cui , Yuchao Tang , Chuanxi Zhu

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

Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…

Optimization and Control · Mathematics 2021-05-12 Hassan Rafique , Mingrui Liu , Qihang Lin , Tianbao Yang

In this work, we address a class of nonconvex nonsmooth optimization problems where the objective function is the sum of two smooth functions (one of which is proximable) and two nonsmooth functions (one proper, closed and proximable, and…

Optimization and Control · Mathematics 2025-03-26 Jan Harold Alcantara , Ching-pei Lee , Akiko Takeda

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate…

Optimization and Control · Mathematics 2018-06-27 Peter Ochs , Jalal Fadili , Thomas Brox

Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…

Optimization and Control · Mathematics 2019-03-26 Jérôme Bolte , Zheng Chen , Edouard Pauwels

This technical note studies a class of distributed nonsmooth convex consensus optimization problem. The cost function is a summation of local cost functions which are convex but nonsmooth. Each of the local cost functions consists of a…

Optimization and Control · Mathematics 2018-08-17 Yue Wei , Hao Fang , Xianlin Zeng , Jie Chen , Panos M. Pardalos

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

Machine Learning · Statistics 2015-06-02 Nicholas G. Polson , James G. Scott , Brandon T. Willard

We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…

Optimization and Control · Mathematics 2019-01-01 Le Thi Khanh Hien , Cuong V. Nguyen , Huan Xu , Canyi Lu , Jiashi Feng

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 work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

Optimization and Control · Mathematics 2016-08-11 Lorenzo Rosasco , Silvia Villa , Bang Công Vũ

We study sampling problems associated with potentials that lack smoothness. The potentials can be either convex or non-convex. Departing from the standard smooth setting, the potentials are only assumed to be weakly smooth or non-smooth, or…

Machine Learning · Computer Science 2023-07-04 Jiaming Liang , Yongxin Chen