Work

A modified inertial proximal minimization algorithm for structured nonconvex and nonsmooth problem

Year: 2024

Type: article

Abstract: We introduce an enhanced inertial proximal minimization algorithm tailored for a category of structured nonconvex and nonsmooth optimization problems. The objective function in question is an aggregation of a smooth function with an associated linear operator, a nonsmooth function dependent on an independent variable, and a mixed function involving two variables. Throughout the iterative procedure, parameters are selected employing a straightforward approach, and weak inertial terms are incorporated into two subproblems within the update sequence. Under a set of lenient conditions, we demonstrate that the sequence engendered by our algorithm is bounded. Furthermore, we establish the global and strong convergence of the algorithmic sequence, contingent upon the assumption that the principal function adheres to the Kurdyka–Łojasiewicz (KL) property. Ultimately, the numerical outcomes corroborate the algorithm’s feasibility and efficacy.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-024-03206-1

Authors: Zhonghui Xue, Qianfeng Ma

Institution: Shanghai Publishing and Printing College

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,990

Funder: National Natural Science Foundation of China