An Augmented Lagrangian method for quasi-equilibrium problems

Autor(es)

Bueno, L. F. ^[1] ; Haeser, G. ^[2] ; Lara, F. ^[3] ; Rojas, F. N. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Sao Paulo, SP - Brazil

^[3] Univ Tarapaca, Dept Matemat, Arica - Chile

^[4] Univ Sao Paulo, Inst Math & Stat, Dept Appl Math, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 76, n. 3, SI, p. 737-766, JUL 2020.
• Citações Web of Science: 2

Resumo

In this paper, we propose an Augmented Lagrangian algorithm for solving a general class of possible non-convex problems called quasi-equilibrium problems (QEPs). We define an Augmented Lagrangian bifunction associated with QEPs, introduce a secondary QEP as a measure of infeasibility and we discuss several special classes of QEPs within our theoretical framework. For obtaining global convergence under a new weak constraint qualification, we extend the notion of an Approximate Karush-Kuhn-Tucker (AKKT) point for QEPs (AKKT-QEP), showing that in general it is not necessarily satisfied at a solution, differently from its counterpart in optimization. We study some particular cases where AKKT-QEP does hold at a solution, while discussing the solvability of the subproblems of the algorithm. We also present illustrative numerical experiments. (AU)

• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/24293-0 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Auxílio à Pesquisa - Regular