Calculus rules of the generalized concave Kurdyka-\L ojasiewicz property

TL;DR

This paper develops new calculus rules for the generalized concave Kurdyka-ojasiewicz property, broadening applicability by removing assumptions on the form and differentiability of desingularizing functions, with implications for optimization theory.

Contribution

It introduces generalized calculus rules for the KL property that do not require specific forms or differentiability of desingularizing functions, extending previous results.

Findings

Rules applicable to broader class of functions

Applicable to nondifferentiable desingularizing functions

Enhances theoretical understanding of KL property

Abstract

In this paper, we propose several calculus rules for the generalized concave Kurdyka-\L ojasiewicz (KL) property, which generalize Li and Pong's results for KL exponents. The optimal concave desingularizing function has various forms and may be nondifferentiable. Our calculus rules do not assume desingularizing functions to have any specific form nor differentiable, while the known results do. Several examples are also given to show that our calculus rules are applicable to a broader class of functions than the known ones.