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arXiv · 2301.10332

Square distance functions are Polyak-{\L}ojasiewicz and vice-versa

Guillaume Garrigos
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Abstract

This short note gathers known results to state that the squared distance function to a (nonconvex) closed set of an Euclidean space is Polyak-{\L}ojasiewicz. As a fuzzy reciprocate, we also recall that every Polyak-{\L}ojasiewicz function can be bounded from below by the squared distance function to its set of minimizers.

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Guillaume Garrigos. 2023-01-24. Square distance functions are Polyak-{\L}ojasiewicz and vice-versa. https://arxiv.org/abs/2301.10332

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