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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 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

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 functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Boosted DC Algorithm, incorporates a line search step to…

Optimization and Control · Mathematics 2020-02-13 Francisco J. Aragón Artacho , Rubén Campoy , Phan T. Vuong

In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. We establish the equivalence between the classical and simplified…

Optimization and Control · Mathematics 2023-05-04 Ronny Bergmann , Orizon P. Ferreira , Elianderson M. Santos , João Carlos O. Souza

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

Optimization and Control · Mathematics 2016-09-22 Fredrik Andersson , Marcus Carlsson , Carl Olsson

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

Optimization and Control · Mathematics 2025-03-25 Xinwei Liu , Vladimir Dvorkin

This paper aims to investigate the effectiveness of the recently proposed Boosted Difference of Convex functions Algorithm (BDCA) when applied to clustering with constraints and set clustering with constraints problems. This is the first…

Optimization and Control · Mathematics 2023-10-24 Tuyen Tran , Kate Figenschou , Phan Tu Vuong

In this work, we propose and analyze DCA-PAGE, a novel algorithm that integrates the difference-of-convex algorithm (DCA) with the ProbAbilistic Gradient Estimator (PAGE) to solve structured nonsmooth difference-of-convex programs. In the…

Optimization and Control · Mathematics 2025-09-16 Anh Duc Nguyen , Alp Yurtsever , Suvrit Sra , Kim-Chuan Toh

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 consider the problem of minimizing a difference-of-convex (DC) function, which can be written as the sum of a smooth convex function with Lipschitz gradient, a proper closed convex function and a continuous possibly nonsmooth concave…

Optimization and Control · Mathematics 2018-04-20 Tianxiang Liu , Ting Kei Pong , Akiko Takeda

We propose a new approach to perform the boosted difference of convex functions algorithm (BDCA) on non-smooth and non-convex problems involving the difference of convex (DC) functions. The recently proposed BDCA uses an extrapolation step…

Optimization and Control · Mathematics 2026-02-05 ZeYu Li , Te Qi , TieYong Zeng

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 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

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…

Statistics Theory · Mathematics 2018-12-19 Shanshan Cao , Xiaoming Huo , Jong-Shi Pang

Bilevel programming has emerged as a valuable tool for hyperparameter selection, a central concern in machine learning. In a recent study by Ye et al. (2023), a value function-based difference of convex algorithm was introduced to address…

Optimization and Control · Mathematics 2024-01-23 Lucy L. Gao , Jane J. Ye , Haian Yin , Shangzhi Zeng , Jin Zhang

Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…

Optimization and Control · Mathematics 2025-12-05 Ting Li , Deren Han , Tanxing Wang , Xingju Cai

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

With the increasing interest in applying the methodology of difference-of-convex (dc) optimization to diverse problems in engineering and statistics, this paper establishes the dc property of many well-known functions not previously known…

Optimization and Control · Mathematics 2019-02-20 Maher Nouiehed , Jong-Shi Pang , Meisam Razaviyayn

This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms…

Optimization and Control · Mathematics 2026-01-07 Zhangcheng Feng , Yancheng Yuan