Various Notions of Nonexpansiveness Coincide for Proximal Mappings of Functions

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-02-09 DOI:10.1137/23m1597009

Honglin Luo, Xianfu Wang, Xinmin Yang

引用次数: 0

Abstract

SIAM Journal on Optimization, Volume 34, Issue 1, Page 642-653, March 2024.
Abstract. Proximal mappings are essential in splitting algorithms for both convex and nonconvex optimization. In this paper, we show that proximal mappings of every prox-bounded function are nonexpansive if and only if they are firmly nonexpansive if and only if they are averaged if and only if the function is convex. Lipschitz proximal mappings of prox-bounded functions are also characterized via hypoconvex or strongly convex functions. Our results generalize a recent result due to Rockafellar.

查看原文本刊更多论文

函数近端映射的各种非扩张性概念相吻合

SIAM 优化期刊》，第 34 卷第 1 期，第 642-653 页，2024 年 3 月。摘要。近似映射在凸优化和非凸优化的拆分算法中都至关重要。本文证明，当且仅当函数为凸函数时，每一个近界函数的近端映射都是非展开的；当且仅当函数为平均函数时，每一个近界函数的近端映射都是坚定的非展开映射。近界函数的 Lipschitz 近似映射也通过下凸或强凸函数来表征。我们的结果概括了 Rockafellar 最近的一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.