Convergence analysis of block majorize-minimize subspace approach

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2023-09-16 DOI:10.1007/s11590-023-02055-z

Emilie Chouzenoux, Jean-Baptiste Fest

引用次数: 3

Abstract

We consider the minimization of a differentiable Lipschitz gradient but non necessarily convex, function F defined on $${\mathbb {R}}^N$$ . We propose an accelerated gradient descent approach which combines three strategies, namely (i) a variable metric derived from the majorization-minimization principle; (ii) a subspace strategy incorporating information from the past iterates; (iii) a block alternating update. Under the assumption that F satisfies the Kurdyka–Łojasiewicz property, we give conditions under which the sequence generated by the resulting block majorize-minimize subspace algorithm converges to a critical point of the objective function, and we exhibit convergence rates for its iterates.

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块最大化-最小化子空间方法的收敛性分析

我们考虑在$${\mathbb {R}}^N$$上定义的可微Lipschitz梯度但不一定是凸的函数F的最小化。我们提出了一种加速梯度下降方法，该方法结合了三种策略，即(i)由最大化-最小化原则导出的变量度量;(ii)包含过去迭代信息的子空间策略;(iii)块交替更新。在F满足Kurdyka -Łojasiewicz性质的假设下，给出了由块最大化最小化子空间算法生成的序列收敛于目标函数的一个临界点的条件，并给出了其迭代的收敛速率。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.