Square distance functions are Polyak-Łojasiewicz and vice-versa
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-Łojasiewicz. As a fuzzy reciprocate, we also recall that every Polyak-Łojasiewicz function can be bounded from below by the squared distance function to its set of minimizers.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- arXiv:
- arXiv:2301.10332
- Bibcode:
- 2023arXiv230110332G
- Keywords:
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- Mathematics - Optimization and Control
- E-Print:
- 8 pages, 2 figures