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In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…

Optimization and Control · Mathematics 2024-10-01 Tan Nhat Pham , Minh N. Dao , Andrew Eberhard , Nargiz Sultanova

Under consideration are multicomponent minimization problems involving a separable nonsmooth convex function penalizing the components individually, and nonsmooth convex coupling terms penalizing linear mixtures of the components. We…

Optimization and Control · Mathematics 2021-08-27 Minh N. Bùi , Patrick L. Combettes , Zev C. Woodstock

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

Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…

Optimization and Control · Mathematics 2019-08-30 Yu-Chao Tang , Chuan-Xi Zhu , Meng Wen , Ji-Gen Peng

Structured convex optimization problems typically involve a mix of smooth and nonsmooth functions. The common practice is to activate the smooth functions via their gradient and the nonsmooth ones via their proximity operator. We show that,…

Optimization and Control · Mathematics 2019-09-11 Patrick L. Combettes , Lilian E. Glaudin

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

Machine Learning · Computer Science 2016-11-17 Luo Luo , Zihao Chen , Zhihua Zhang , Wu-Jun Li

The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…

Optimization and Control · Mathematics 2025-05-29 Tan Nhat Pham , Minh N. Dao , Nima Amjady , Rakibuzzaman Shah

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 focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…

Optimization and Control · Mathematics 2023-11-09 Ruyu Liu , Shaohua Pan , Yuqia Wu , Xiaoqi Yang

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function so that along the iterations the objective function decreases. Such a simple principle allows to solve a large…

Optimization and Control · Mathematics 2025-03-04 Ion Necoara , Daniela Lupu

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

We investigate an inertial algorithm of gradient type in connection with the minimization of a nonconvex differentiable function. The algorithm is formulated in the spirit of Nesterov's accelerated convex gradient method. We prove some…

Functional Analysis · Mathematics 2020-02-11 Szilárd Csaba László

We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…

Optimization and Control · Mathematics 2025-01-22 Damek Davis , Dmitriy Drusvyatskiy , Zhan Shi

This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…

Optimization and Control · Mathematics 2026-03-25 Hong Zhu , Xun Qian

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…

Optimization and Control · Mathematics 2015-04-24 A. S. Lewis , S. J. Wright

In this paper, we study a class of nonconvex and nonsmooth structured difference-of-convex (DC) programs, which contain in the convex part the sum of a nonsmooth linearly composed convex function and a differentiable function, and in the…

Optimization and Control · Mathematics 2025-05-06 Radu Ioan Bot , Rossen Nenov , Min Tao

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

Optimization and Control · Mathematics 2026-03-25 Geng-Hua Li , Hai-Yi Zhao , Xiangkai Sun

In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…

Optimization and Control · Mathematics 2024-12-02 Lahcen El Bourkhissi , Ion Necoara

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

We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…

Optimization and Control · Mathematics 2023-05-01 Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz