The local minimality of differentiable functions
Optimization and Control
2026-02-17 v1
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.
Cite
@article{arxiv.2602.13965,
title = {The local minimality of differentiable functions},
author = {Tien-Son Pham},
journal= {arXiv preprint arXiv:2602.13965},
year = {2026}
}