Frugal and decentralised resolvent splittings defined by nonexpansive operators

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2023-10-05 DOI:10.1007/s11590-023-02064-y

Matthew K. Tam

引用次数: 0

Abstract

Abstract Frugal resolvent splittings are a class of fixed point algorithms for finding a zero in the sum of the sum of finitely many set-valued monotone operators, where the fixed point operator uses only vector addition, scalar multiplication and the resolvent of each monotone operator once per iteration. In the literature, the convergence analyses of these schemes are performed in an inefficient, algorithm-by-algorithm basis. In this work, we address this by developing a general framework for frugal resolvent splitting which simultaneously covers and extends several important schemes in the literature. The framework also yields a new resolvent splitting algorithm which is suitable for decentralised implementation on regular networks.

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由非扩张运营商定义的节俭和分散的解决方案分裂

摘要节俭分解算法是一类求有限多个集值单调算子和的和为零的不动点算法，其中不动点算子每次迭代只使用向量加法、标量乘法和每个单调算子的分解算子一次。在文献中，这些方案的收敛性分析是在低效的、逐算法的基础上进行的。在这项工作中，我们通过开发节俭解决分裂的一般框架来解决这个问题，该框架同时涵盖并扩展了文献中的几个重要方案。该框架还提出了一种新的分解算法，适用于在常规网络上的去中心化实现。

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.