A Bregman proximal subgradient algorithm for nonconvex and nonsmooth fractional optimization problems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-05-16 DOI:10.1016/j.apnum.2024.05.006

Xian Jun Long , Xiao Ting Wang , Gao Xi Li , Geng Hua Li

引用次数: 0

Abstract

In this paper, we study a class of nonconvex and nonsmooth fractional optimization problem, where the numerator of which is the sum of a nonsmooth and nonconvex function and a relative smooth nonconvex function, while the denominator is relative weakly convex nonsmooth function. We propose a Bregman proximal subgradient algorithm for solving this type of fractional optimization problems. Under moderate conditions, we prove that the subsequence generated by the proposed algorithm converges to a critical point, and the generated sequence globally converges to a critical point when the objective function satisfies the Kurdyka-Łojasiewicz property. We also obtain the convergence rate of the proposed algorithm. Finally, two numerical experiments illustrate the effectiveness and superiority of the algorithm. Our results give a positive answer to an open problem proposed by Bot et al. [14].

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非凸和非光滑分数优化问题的布雷格曼近似子梯度算法

本文研究了一类非凸非光滑分式优化问题，其分子为非光滑非凸函数与相对光滑非凸函数之和，分母为相对弱凸非光滑函数。我们提出了一种 Bregman 近似子梯度算法来求解这类分数优化问题。在适度条件下，我们证明了当目标函数满足 Kurdyka-Łojasiewicz 特性时，所提算法生成的子序列会收敛到临界点，并且生成的序列会全局收敛到临界点。我们还得出了所提算法的收敛速率。最后，两个数值实验说明了算法的有效性和优越性。我们的结果为 Bot 等人提出的一个开放性问题给出了积极的答案[14]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.