Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2023-11-20 DOI:10.1007/s11228-023-00702-2

Rubén Campoy

引用次数: 0

Abstract

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility problems defined by finitely many sets, some other require the use of a product space reformulation to construct equivalent problems with two sets. In this work we analyze how some regularity properties are preserved under a reformulation in a product space of reduced dimension. This allows us to establish local linear convergence of parallel projection methods which are constructed through this reformulation.

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降维积空间重构下集合的正则性

关于集合的正则性和集合集合的正则性的不同概念在分析非凸情形下投影算法的收敛性时起着重要的作用。虽然一些投影算法可以应用于由有限多个集合定义的可行性问题，但其他一些则需要使用积空间重构来构造具有两个集合的等效问题。在本文中，我们分析了在降维积空间中，一些正则性是如何在重新表述下保持的。这允许我们建立局部线性收敛的平行投影方法，这是构造通过这个重新表述。

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

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.