Work

Convergence of ZH-Type Nonmonotone Descent Method for Kurdyka–Łojasiewicz Optimization Problems

Year: 2025

Type: article

Abstract: . We propose a novel iterative framework for minimizing a proper lower semicontinuous Kurdyka–Łojasiewicz (KL) function [Formula: see text]. It comprises a Zhang–Hager (ZH-type) nonmonotone decrease condition and a relative error condition. Hence, the sequence generated by the ZH-type nonmonotone descent methods will fall within this framework. Any sequence conforming to this framework is proved to converge to a critical point of [Formula: see text]. If in addition [Formula: see text] has the KL property of exponent [Formula: see text] at the critical point, the convergence has a linear rate for [Formula: see text] and a sublinear rate of exponent [Formula: see text] for [Formula: see text]. To the best of our knowledge, this is the first work to establish the full convergence of the iterate sequence generated by a ZH-type nonmonotone descent method for nonconvex and nonsmooth optimization problems. The obtained results are also applied to achieve the full convergence of the iterate sequences produced by the proximal gradient method and Riemannian gradient method with the ZH-type nonmonotone line-search.

Source: SIAM Journal on Optimization

DOI: 10.1137/24m1669153

Authors: Yitian Qian, Ting Tao, Shaohua Pan, Houduo Qi

Institutions: Hong Kong Polytechnic University, Foshan University, South China University of Technology

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province, Hong Kong Polytechnic University

Awards: G1808301013, G4401708612, G4904472146, G693560886