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

TL;DR

This paper establishes a fundamental equivalence between squared distance functions and Polyak-{\

Contribution

It demonstrates that squared distance functions are Polyak-{\

Findings

Squared distance functions are Polyak-{\

Polyak-{\

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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.