OPTIMALITY CONDITIONS AND CONSTRAINT QUALIFICATIONS FOR GENERALIZED NASH EQUILIBRIUM PROBLEMS AND THEIR PRACTICAL IMPLICATIONS

Autor(es)

Bueno, Luis Felipe ^[1] ; Haeser, Gabriel ^[2] ; Rojas, Frank Navarro ^[2]

Afiliação do(s) autor(es)

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

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

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 29, n. 1, p. 31-54, 2019.
• Citações Web of Science: 3

Resumo

Generalized Nash equilibrium problems (GNEPs) are a generalization of the classic Nash equilibrium problems (NEPs), where each player's strategy set depends on the choices of the other players. In this work we study constraint qualifications (CQs) and optimality conditions tailored for GNEPs, and we discuss their relations and implications for global convergence of algorithms. We show the surprising fact that, in contrast to the case of nonlinear programming, in general the Karush-Kuhn-Tucker (KKT) residual cannot be made arbitrarily small near a solution of a GNEP. We then discuss some important practical consequences of this fact. We also prove that this phenomenon is not present in an important class of GNEPs, including NEPs. Finally, under an introduced weak CQ, we prove global convergence to a KKT point of an augmented Lagrangian algorithm for GNEPs, and under the quasi-normality (QN) CQ for GNEPs, we prove boundedness of the dual sequence. (AU)

• Processo FAPESP: 15/02528-8 - Métodos do tipo Newton para otimização linear e não linear
• Beneficiário: Luis Felipe Cesar da Rocha Bueno
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático