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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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Advanced Banach Space Theory