This paper presents a new application of Borsuk-Ulam's theorem to nonlinear programming

2023/08/26 by Hidefumi Kawasaki, Kawasaki, Hidefumi
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2308.13748

Abstract

Borsuk-Ulam's theorem is a useful tool of algebraic topology. It states that for any continuous mapping f from the n-sphere to the n-dimensional Euclidean space, there exists a pair of antipodal points such that f(x)=f(-x). As for its applications, ham-sandwich theorem, necklace theorem and coloring of Kneser graph by Lovász are well-known. This paper attempts to apply Borsuk-Ulam's theorem to nonlinear programming.

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