Work

A Projected Inexact Levenberg-Marquardt Method for the Completely Positive Matrix Factorization

Year: 2026

Type: article

Abstract: In this work we propose and analyze a projected Levenberg–Marquardt method for solving completely positive matrix factorization problems. Instead of computing the exact Levenberg–Marquardt direction, we introduce an inexact direction which simplifies the calculations and reduces the computational cost. Global convergence results are established for the proposed method endowed with a non-monotone line search. A series of numerical experiments on different classes of the problem are carried out and indicate that the new Projected Inexact Levenberg–Marquardt algorithm is competitive with well-established alternatives such as algorithms based on proximal gradient or alternating minimization methods.

Source: Journal of Optimization Theory and Applications

DOI: 10.1007/s10957-026-02950-2

Authors: Roger Behling, Douglas Gonçalves, Hugo Lara, Harry Oviedo

Institutions: Universidade Federal de Santa Catarina, Adolfo Ibáñez University

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina