坚定非展开映射组成的强收敛性

IF 1.8 3区数学 Q1 Mathematics

Journal of Global Optimization Pub Date : 2024-07-27 DOI:10.1007/s10898-024-01417-w

José Márcio Machado de Brito, João Xavier da Cruz Neto, Ítalo Dowell Lira Melo

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引用次数: 0

摘要

在本文中，我们提供了一个必要条件和充分条件，在这个条件下，p-均匀凸空间中有限多个坚定非展开映射的组合会强收敛。特别是，我们得到了 CAT(\(\kappa \))空间中交替投影法的收敛结果，其中 \(\kappa \ge 0\).我们还研究了在坚定的非膨胀映射满足误差约束，并且这些映射的定点集合是有界线性规则的情况下，该方法所产生的序列的收敛率。

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Strong convergence of the composition of firmly nonexpansive mappings

In this paper, we provide a necessary and sufficient condition under which the compositions of finitely many firmly nonexpansive mappings in a p-uniformly convex space converge strongly. In particular, we obtain convergence results for the method of alternating projections in CAT(\(\kappa \)) spaces, with \(\kappa \ge 0\). We also study the rate of convergence of the sequence generated by the method in cases where the firmly nonexpansive mappings satisfy an error bound, and the set of fixed points of these mappings is boundedly linearly regular.

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来源期刊

Journal of Global Optimization 数学-应用数学

CiteScore

0.10

自引率

5.60%

发文量

137

审稿时长

6 months

期刊介绍： The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.