English
Related papers

Related papers: Improved convergence rates for the Difference-of-C…

200 papers

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

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

In this paper, we study the convergence rate of the DCA (Difference-of-Convex Algorithm), also known as the convex-concave procedure, with two different termination criteria that are suitable for smooth and nonsmooth decompositions…

Optimization and Control · Mathematics 2023-02-24 Hadi Abbaszadehpeivasti , Etienne de Klerk , Moslem Zamani

The difference-of-convex algorithm (DCA) is a well-established nonlinear programming technique that solves successive convex optimization problems. These sub-problems are obtained from the difference-of-convex~(DC) decompositions of the…

Optimization and Control · Mathematics 2026-02-20 Hadi Abbaszadehpeivasti , Etienne de Klerk , Adrien Taylor

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 a simple proof of the worst-case iteration complexity for the Difference of Convex functions Algorithm (DCA) for unconstrained minimization, showing that the global rate of convergence of the norm of the objective function's…

Optimization and Control · Mathematics 2026-01-23 Serge Gratton , Philippe L. Toint

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

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

We propose an algorithm for optimizing the parameters of single hidden layer neural networks. Specifically, we derive a blockwise difference-of-convex (DC) functions representation of the objective function. Based on the latter, we propose…

Machine Learning · Computer Science 2024-01-17 Daniel Tschernutter , Mathias Kraus , Stefan Feuerriegel

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

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

In this paper, we propose a clean and general proof framework to establish the convergence analysis of the Difference-of-Convex (DC) programming algorithm (DCA) for both standard DC program and convex constrained DC program. We first…

Optimization and Control · Mathematics 2022-11-22 Yi-Shuai Niu

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

The paper deals with stochastic difference-of-convex functions (DC) programs, that is, optimization problems whose the cost function is a sum of a lower semicontinuous DC function and the expectation of a stochastic DC function with respect…

Numerical Analysis · Mathematics 2020-12-14 Le Thi Hoai An , Huynh Van Ngai , Pham Dinh Tao , Luu Hoang Phuc Hau

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

Machine Learning · Statistics 2025-02-04 Yasi Zhang , Oscar Leong

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 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

In this paper we consider the difference-of-convex (DC) programming problems, whose objective function is the difference of two convex functions. The classical DC Algorithm (DCA) is well-known for solving this kind of problems, which…

Optimization and Control · Mathematics 2022-04-27 Yu You , Yi-Shuai Niu

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

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
‹ Prev 1 2 3 10 Next ›