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Borsuk-Ulam's theorem is a useful tool of algebraic topology. It states thatfor any continuous mapping $f$ from the $n$-sphere to the $n$-dimensionalEuclidean space, there exists a pair of antipodal points such that$f(x)=f(-x)$. As for its applications, ham-sandwich theorem, necklace theoremand coloring of Kneser graph by Lov\'{a}sz are well-known. This paper attemptsto apply Borsuk-Ulam's theorem to nonlinear programming.

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