凸可行性问题的有限收敛圆心法

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-07-15 DOI:10.1137/23m1595412

Roger Behling, Yunier Bello-Cruz, Alfredo N. Iusem, Di Liu, Luiz-Rafael Santos

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引用次数: 0

摘要

SIAM 优化期刊》，第 34 卷第 3 期，第 2535-2556 页，2024 年 9 月。摘要本文提出了凸可行性问题（CFP）圆周中心法的一种变体，在 Slater 假设下确保有限收敛。该方法用在分离半空间上的投影代替在凸集上的精确投影。如果扰动参数的下降速度足够慢，例如发散级数的项，就会实现有限收敛。据我们所知，这是第一种能保证有限收敛的 CFP 圆心方法。

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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A Finitely Convergent Circumcenter Method for the Convex Feasibility Problem

SIAM Journal on Optimization, Volume 34, Issue 3, Page 2535-2556, September 2024.
Abstract. In this paper, we present a variant of the circumcenter method for the convex feasibility problem (CFP), ensuring finite convergence under a Slater assumption. The method replaces exact projections onto the convex sets with projections onto separating half-spaces, perturbed by positive exogenous parameters that decrease to zero along the iterations. If the perturbation parameters decrease slowly enough, such as the terms of a diverging series, finite convergence is achieved. To the best of our knowledge, this is the first circumcenter method for CFP that guarantees finite convergence.

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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.