球面梯度投影法、互补问题和共正性

IF 1.8 3区数学 Q1 Mathematics

Journal of Global Optimization Pub Date : 2024-04-16 DOI:10.1007/s10898-024-01390-4

Orizon Pereira Ferreira, Yingchao Gao, Sándor Zoltán Németh, Petra Renáta Rigó

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引用次数: 0

摘要

通过使用恒定步长，提出了封闭球凸集的球面梯度投影法的收敛性分析。该算法可用于讨论算子关于圆锥的共存性。这种方法也可用于分析非线性圆锥互补问题的可解性。据我们所知，这是第一种与正半定锥的算子共存性有关的数值方法。此外，还提供了有关算子共存性的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Gradient projection method on the sphere, complementarity problems and copositivity

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Gradient projection method on the sphere, complementarity problems and copositivity

By using a constant step-size, the convergence analysis of the gradient projection method on the sphere is presented for a closed spherically convex set. This algorithm is applied to discuss copositivity of operators with respect to cones. This approach can also be used to analyse solvability of nonlinear cone-complementarity problems. To our best knowledge this is the first numerical method related to the copositivity of operators with respect to the positive semidefinite cone. Numerical results concerning the copositivity of operators are also provided.

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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.