\L ojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures
Algebraic Geometry
2020-01-31 v2 Optimization and Control
Abstract
In this paper, we give some {\L}ojasiewicz-type inequalities and a nonsmooth slope inequality on non-compact domains for continuous definable functions in an o-minimal structure. We also give a necessary and sufficicent condition for which global error bound exists. Moreover, we point out the relationship between the Palais-Smale condition and this global error bound.
Keywords
Cite
@article{arxiv.1303.2199,
title = {\L ojasiewicz-type inequalities and global error bounds for nonsmooth definable functions in o-minimal structures},
author = {Hoang Phi Dũng},
journal= {arXiv preprint arXiv:1303.2199},
year = {2020}
}
Comments
14 pages