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arXiv · 2308.13748

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

Hidefumi Kawasaki
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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 Lov\'{a}sz are well-known. This paper attempts to apply Borsuk-Ulam's theorem to nonlinear programming.

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Hidefumi Kawasaki. 2023-08-26. This paper presents a new application of Borsuk-Ulam's theorem to nonlinear programming. https://arxiv.org/abs/2308.13748

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