Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods

In this paper, we study the Kurdyka–Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with kno...

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Bibliographic Details
Published in:	Foundations of computational mathematics Vol. 18; no. 5; pp. 1199 - 1232
Main Authors:	Li, Guoyin, Pong, Ting Kei
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.10.2018 Springer Nature B.V
Subjects:	Algorithms Applications of Mathematics Calculus Computer Science Convergence Economics Error analysis Exponents Least squares method Linear and Multilinear Algebras Math Applications in Computer Science Mathematical models Mathematics Mathematics and Statistics Matrix Theory Minimax technique Nonlinear programming Numerical Analysis Optimization Recovery Regression analysis Regularization Sparse optimization Linear convergence Luo–Tseng error bound 90C25 Convergence rate 90C26 90C05 First-order methods Kurdyka–Łojasiewicz inequality
ISSN:	1615-3375, 1615-3383
Online Access:	Get full text
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