A unified approach for smoothing approximations to the exact l₁-penalty for inequality-constrained optimization

Autor(es)

da Rosa, Mariana ; Ribeiro, Ademir Alves ; Karas, Elizabeth Wegner

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. N/A, p. 18-pg., 2025-05-26.

Resumo

In penalty methods for inequality-constrained optimization problems, the nondifferentiability of the exact l(1)-penalty function limits the use of efficient smooth algorithms for solving the subproblems. In light of this, a great number of smoothing techniques has been proposed in the literature. In this paper we present, in a unified manner, results and methods based on functions that smooth and approximate the exact penalty function. We show that these functions define a class of algorithms that converges to global and local minimizers. This unified approach allows us to derive sufficient conditions that guarantee the existence of local minimizers for the subproblems and to establish a linear convergence rate for this class of methods, using an error bound-type condition. Finally, numerical experiments with problems of the CUTEst collection are presented to illustrate the computational performance of some methods from the literature which can be recovered as particular cases of our unified approach. (AU)

• Processo FAPESP: 22/06745-7 - Métodos de Lagrangiano aumentado para otimização com restrições usando penalização exata diferenciável
• Beneficiário: Mariana da Rosa
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 24/15980-5 - Integração de Métodos Contínuos e Discretos de Otimização no Problema de Geometria de Distâncias com Incertezas nos Dados
• Beneficiário: Mariana da Rosa
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado