Work

Local convergence of a proximal type method for weakly convex minimization

Year: 2026

Type: article

Abstract: The main purpose of this paper is to develop and analyze a proximal-type method for the local minimization of weakly convex functions. Our motivation for introducing this algorithm is to increase its versatility and applicability in a broader range of scenarios in optimization and introduce a more adaptable version of the method for typical generalizations. Our study relies heavily on the Moreau envelope, a well-known mathematical tool used to analyze the behavior of the proximal operator. By leveraging the properties of the Moreau envelope, we are able to prove that the proximal algorithm converges in local contexts. Moreover, we present a complexity result to assess the practical feasibility of the proximal algorithm and provide a numerical example to illustrate the practical behavior of the algorithm.

Source: Computational and Applied Mathematics

DOI: 10.1007/s40314-026-03952-6

Authors: Valdinês Leite de Sousa Júnior, Lucas Vidal de Meireles, Samara Costa Lima, Gilson do Nascimento Silva

Institutions: Universidade Federal do Cariri, Universidade Federal do Piauí

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funder: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior