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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

We consider a class of difference-of-convex (DC) optimization problems whose objective is level-bounded and is the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous concave function.…

Optimization and Control · Mathematics 2017-06-23 Bo Wen , Xiaojun Chen , Ting Kei Pong

In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a DC (Difference of Convex functions) function, where the differentiable function is not restricted to the global Lipschitz gradient…

Optimization and Control · Mathematics 2021-06-10 Duy Nhat Phan , Hoai An Le Thi

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

We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…

Optimization and Control · Mathematics 2019-11-12 Hoai An Le Thi , Hoai Minh Le , Duy Nhat Phan , Bach Tran

The difference-of-convex algorithm (DCA) is a conceptually simple method for the minimization of (possibly) nonconvex functions that are expressed as the difference of two convex functions. At each iteration, DCA constructs a global…

Optimization and Control · Mathematics 2023-06-06 Chaorui Yao , Xin Jiang

Standard approaches to difference-of-convex (DC) programs require exact solution to a convex subproblem at each iteration, which generally requires noiseless computation and infinite iterations of an inner iterative algorithm. To tackle…

Optimization and Control · Mathematics 2025-09-17 Yi Zhang , Isao Yamada

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

In this paper, we consider a class of single-ratio fractional minimization problems, where both the numerator and denominator of the objective are convex functions satisfying positive homogeneity. Many nonsmooth optimization problems on the…

Optimization and Control · Mathematics 2025-10-23 Anna Qi , Jianfeng Huang , Lihua Yang , Chao Huang

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of…

Optimization and Control · Mathematics 2022-09-27 Shota Takahashi , Mituhiro Fukuda , Mirai Tanaka

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 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 introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For $n$ coordinate-blocks and $k$ iterations, our main result proves a…

Optimization and Control · Mathematics 2025-12-01 Hoomaan Maskan , Paniz Halvachi , Suvrit Sra , Alp Yurtsever

We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…

Optimization and Control · Mathematics 2025-09-03 Mootta Prangprakhon , Nimit Nimana

We establish new theoretical convergence guarantees for the difference-of-convex algorithm (DCA), where the second function is allowed to be weakly-convex, measuring progress via composite gradient mapping. Based on a tight analysis of two…

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

Difference-of-Convex Algorithm (DCA) is a well-known nonconvex optimization algorithm for minimizing a nonconvex function that can be expressed as the difference of two convex ones. Many famous existing optimization algorithms, such as SGD…

Machine Learning · Computer Science 2024-12-16 Youran Sun , Yihua Liu , Yi-Shuai Niu

This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…

Optimization and Control · Mathematics 2023-03-07 Luyao Guo , Xinli Shi , Jinde Cao , Zihao Wang

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 paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an inexact adaptive counterpart of the well-recognized DCA…

Optimization and Control · Mathematics 2026-01-13 P. D. Khanh , V. V. H. Khoa , B. S. Mordukhovich , D. B. Tran , N. V. Vo