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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

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction…

Optimization and Control · Mathematics 2017-07-24 Francisco J. Aragón Artacho , Ronan M. T. Fleming , Phan T. Vuong

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

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

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

Augmenting algorithms with learned predictions is a promising approach for going beyond worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have demonstrated that a warm start with learned dual solutions can improve…

Machine Learning · Computer Science 2022-05-23 Shinsaku Sakaue , Taihei Oki

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

The Boosted Difference of Convex functions Algorithm (BDCA) was recently proposed for minimizing smooth difference of convex (DC) functions. BDCA accelerates the convergence of the classical Difference of Convex functions Algorithm (DCA)…

Optimization and Control · Mathematics 2019-07-24 Francisco J. Aragón Artacho , Phan T. Vuong

This paper considers convex optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for…

Optimization and Control · Mathematics 2015-06-16 Aryan Mokhtari , Alejandro Ribeiro

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

Minimizing the difference of two submodular (DS) functions is a problem that naturally occurs in various machine learning problems. Although it is well known that a DS problem can be equivalently formulated as the minimization of the…

Machine Learning · Computer Science 2024-04-08 Marwa El Halabi , George Orfanides , Tim Hoheisel

The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of Convex functions Algorithm (DCA). This acceleration is achieved thanks to an extrapolation…

Optimization and Control · Mathematics 2022-08-03 Francisco J. Aragón Artacho , Rubén Campoy , Phan T. Vuong

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

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

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 paper, we introduce an inexact approach to the Boosted Difference of Convex Functions Algorithm (BDCA) for solving nonconvex and nondifferentiable problems involving the difference of two convex functions (DC functions).…

Optimization and Control · Mathematics 2024-12-10 Orizon P. Ferreira , Boris S. Mordukhovich , Wilkreffy M. S. Santos , João Carlos O. Souza

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 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

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

Gradient-based optimization methods for hyperparameter tuning guarantee theoretical convergence to stationary solutions when for fixed upper-level variable values, the lower level of the bilevel program is strongly convex (LLSC) and smooth…

Optimization and Control · Mathematics 2022-06-14 Lucy Gao , Jane J. Ye , Haian Yin , Shangzhi Zeng , Jin Zhang