The exact modulus of the generalized concave Kurdyka-{\L}ojasiewicz property
Optimization and Control
2021-10-15 v5
Abstract
We introduce a generalized version of the concave Kurdyka-\L ojasiewicz (KL) property by employing nonsmooth desingularizing functions. We also present the exact modulus of the generalized concave KL property, which provides an answer to the open question regarding the optimal concave desingularizing function. The exact modulus is designed to be the smallest among all possible concave desingularizing functions. Examples are given to illustrate this pleasant property. In turn, using the exact modulus we provide the sharpest upper bound for the total length of iterates generated by the celebrated Bolte-Sabach-Teboulle PALM algorithm.
Keywords
Cite
@article{arxiv.2008.13257,
title = {The exact modulus of the generalized concave Kurdyka-{\L}ojasiewicz property},
author = {Xianfu Wang and Ziyuan Wang},
journal= {arXiv preprint arXiv:2008.13257},
year = {2021}
}
Comments
To appear on Mathematics of Operations Research. Fixed a display error in the previous version