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There is an existing exact algorithm that solves DC programming problems if one component of the DC function is polyhedral convex (Loehne, Wagner, 2017). Motivated by this, first, we consider two cutting-plane algorithms for generating an…

Optimization and Control · Mathematics 2023-09-12 Fahaar Mansoor Pirani , Firdevs Ulus

In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm…

Data Structures and Algorithms · Computer Science 2011-08-23 Yoshinobu Kawahara , Takashi Washio

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

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 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

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

This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality…

Optimization and Control · Mathematics 2016-07-13 Zhong Jin , David Y Gao

In this paper, we consider a class of nonconvex (not necessarily differentiable) optimization problems called generalized DC (Difference-of-Convex functions) programming, which is minimizing the sum of two separable DC parts and one…

Optimization and Control · Mathematics 2023-08-07 Hongjin He , Zhiyuan Zhang

We introduce a novel algorithm for solving learning problems where both the loss function and the regularizer are non-convex but belong to the class of difference of convex (DC) functions. Our contribution is a new general purpose proximal…

Machine Learning · Computer Science 2015-07-03 Alain Rakotomamonjy , Remi Flamary , Gilles Gasso

We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the…

Optimization and Control · Mathematics 2026-03-16 Zhiping Li , Nan Jiang , Rujun Jiang

We introduce a new approach to apply the boosted difference of convex functions algorithm (BDCA) for solving non-convex and non-differentiable problems involving difference of two convex functions (DC functions). Supposing the first DC…

Optimization and Control · Mathematics 2022-06-22 Orizon P. Ferreira , Elianderson M. Santos , João Carlos O. Souza

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…

Optimization and Control · Mathematics 2022-04-21 Jingyi Wang , Cosmin G. Petra

We consider the problem of maximizing a convex quadratic function over a bounded polyhedral set. We design a new framework based on SDP relaxations and cutting plane methods for solving the associated reference value problem. The major…

Optimization and Control · Mathematics 2025-04-28 Zheng Qu , Tianyou Zeng , Yuchen Lou

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

A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference $f=g-h$ of two convex functions $g$ and $h$. In particular, we deal with the special case where one…

Optimization and Control · Mathematics 2017-04-06 Andreas Löhne , Andrea Wagner

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

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An…

Optimization and Control · Mathematics 2016-10-21 Sebastian Banert , Radu Ioan Bot

This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…

Optimization and Control · Mathematics 2023-02-10 Rafael Correa , Marco A. López , Pedro Pérez-Aros

Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC…

Numerical Analysis · Computer Science 2014-07-23 Hoai An Le Thi , Tao Pham Dinh , Hoai Minh Le , Xuan Thanh Vo