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arXiv · 2602.13965

The local minimality of differentiable functions

Tien-Son Pham
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Abstract

In this paper we present necessary and sufficient conditions (in terms of {\L}ojasiewicz inequalities) for the stability of local minimum points in smooth unconstrained optimization. In particular, we derive a sufficient condition for which the local minimum property of a given function is determined by its Taylor polynomial of a certain degree.

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Tien-Son Pham. 2026-02-15. The local minimality of differentiable functions. https://arxiv.org/abs/2602.13965

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