Convex optimization on CAT(0) cubical complexes

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-01-21 DOI:10.1016/j.aam.2025.102849

Ariel Goodwin , Adrian S. Lewis , Genaro López-Acedo , Adriana Nicolae

引用次数: 0

Abstract

We consider geodesically convex optimization problems involving distances to a finite set of points A in a CAT(0) cubical complex. Examples include the minimum enclosing ball problem, the weighted mean and median problems, and the feasibility and projection problems for intersecting balls with centers in A. We propose a decomposition approach relying on standard Euclidean cutting plane algorithms. The cutting planes are readily derivable from efficient algorithms for computing geodesics in the complex.

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CAT(0)立方配合物的凸优化

研究了CAT(0)三次复形中涉及到有限点a的距离的测地线凸优化问题。例子包括最小围球问题、加权均值和中值问题以及a中有中心相交球的可行性和投影问题。我们提出了一种基于标准欧几里德切割平面算法的分解方法。切割平面很容易从计算复杂测地线的有效算法中推导出来。

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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.