Square distance functions are Polyak-{\L}ojasiewicz and vice-versa
Optimization and Control
2023-01-26 v1
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.
Cite
@article{arxiv.2301.10332,
title = {Square distance functions are Polyak-{\L}ojasiewicz and vice-versa},
author = {Guillaume Garrigos},
journal= {arXiv preprint arXiv:2301.10332},
year = {2023}
}
Comments
8 pages, 2 figures