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Related papers: The Boosted DC Algorithm for nonsmooth functions

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We address the problem of computing stationary points for non-smooth, non-convex optimization problems. While this topic is well studied in the smooth setting, fewer algorithmic and theoretical results exist for the non-smooth case. Within…

Optimization and Control · Mathematics 2026-05-18 Hoai An Le Thi , Van Ngai Huynh , Tao Pham Dinh

We study the continuous-time structure of the difference-of-convex algorithm (DCA) for smooth DC decompositions with a strongly convex component. In dual coordinates, classical DCA is exactly the full-step explicit Euler discretization of a…

Optimization and Control · Mathematics 2026-04-09 Yi-Shuai Niu

This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge function. This includes proving the existence of global…

Optimization and Control · Mathematics 2024-09-23 Vo Si Trong Long , Nguyen Mau Nam , Tuyen Tran , Nguyen Thi Thu Van

In this paper, we present two variants of DCA (Different of Convex functions Algorithm) to solve the constrained sum of differentiable function and composite functions minimization problem, with the aim of increasing the convergence speed…

Optimization and Control · Mathematics 2018-06-27 Hoai An Le Thi , Hoai Minh Le , Duy Nhat Phan , Bach Tran

In this paper, we consider a class of difference-of-convex (DC) optimization problems, which require only a weaker restricted $L$-smooth adaptable property on the smooth part of the objective function, instead of the standard global…

Optimization and Control · Mathematics 2025-04-30 Lei Yang , Jingjing Hu , Kim-Chuan Toh

We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight…

Optimization and Control · Mathematics 2026-01-23 Teodor Rotaru , Panagiotis Patrinos , François Glineur

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc)…

Optimization and Control · Mathematics 2015-11-06 Jong-Shi Pang , Meisam Razaviyayn , Alberth Alvarado

We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…

Optimization and Control · Mathematics 2017-01-31 Katsuya Tono , Akiko Takeda , Jun-ya Gotoh

The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…

Optimization and Control · Mathematics 2025-05-19 Songnian He , Qiao-Li Dong , Michael Th. Rassias

We propose and study a version of the DCA (Difference-of-Convex functions Algorithm) using the $\ell_1$ penalty function for solving nonsmooth DC optimization problems with nonsmooth DC equality and inequality constraints. The method…

Optimization and Control · Mathematics 2024-04-23 M. V. Dolgopolik

We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…

Optimization and Control · Mathematics 2024-03-26 Teodor Rotaru , Panagiotis Patrinos , François Glineur

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

Stochastic algorithms are well-known for their performance in the era of big data. In convex optimization, stochastic algorithms have been studied in depth and breadth. However, the current body of research on stochastic algorithms for…

Optimization and Control · Mathematics 2021-08-06 Hoai An Le Thi , Hoang Phuc Hau Luu , Tao Pham Dinh

Consider the problem of minimizing the sum of a smooth (possibly non-convex) and a convex (possibly nonsmooth) function involving a large number of variables. A popular approach to solve this problem is the block coordinate descent (BCD)…

Optimization and Control · Mathematics 2014-11-03 Meisam Razaviyayn , Mingyi Hong , Zhi-Quan Luo , Jong-Shi Pang

Difference of convex (DC) functions cover a broad family of non-convex and possibly non-smooth and non-differentiable functions, and have wide applications in machine learning and statistics. Although deterministic algorithms for DC…

Optimization and Control · Mathematics 2019-02-05 Yi Xu , Qi Qi , Qihang Lin , Rong Jin , Tianbao Yang

This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…

Optimization and Control · Mathematics 2025-03-14 Zixuan Liu , Xuyang Wu , Dandan Wang , Jie Lu

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class…

Optimization and Control · Mathematics 2025-06-10 Minh N. Dao , Tan Nhat Pham , Phan Thanh Tung

Imaging tasks are typically tackled using a structured optimization framework. This paper delves into a class of algorithms for difference-of-convex (DC) structured optimization, focusing on minimizing a DC function along with a possibly…

Optimization and Control · Mathematics 2024-09-19 Tsz Ching Chow , Chaoyan Huang , Zhongming Wu , Tieyong Zeng , Angelica I. Aviles-Rivero

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…

Optimization and Control · Mathematics 2019-07-24 Sandeep Kumar , Ketan Rajawat , Daniel P. Palomar

This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy…

Optimization and Control · Mathematics 2026-02-18 Ran Zhang , Hongpeng Sun