NEW SEQUENTIAL OPTIMALITY CONDITIONS FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS AND ALGORITHMIC CONSEQUENCES

Autor(es)

Andreani, R. ^[1] ; Haeser, G. ^[2] ; Secchin, L. D. ^[3] ; Silva, P. J. S. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Appl Math, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Fed Espirito Santo, Dept Appl Math, Rodovia BR 101, Km 60, BR-29932540 Sao Mateus, ES - Brazil

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 29, n. 4, p. 3201-3230, 2019.
• Citações Web of Science: 2

Resumo

In recent years, the theoretical convergence of iterative methods for solving nonlinear constrained optimization problems has been addressed using sequential optimality conditions, which are satisfied by minimizers independently of constraint qualifications (CQs). Even though there is a considerable literature devoted to sequential conditions for standard nonlinear optimization, the same is not true for mathematical programs with complementarity constraints (MPCCs). In this paper, we show that the established sequential optimality conditions are not suitable for the analysis of convergence of algorithms for MPCC. We then propose new sequential optimality conditions for usual stationarity concepts for MPCC, namely, weak, Clarke, and Mordukhovich stationarity. We call these conditions AW-, AC-, and AM-stationarity, respectively. The weakest MPCC-tailored CQs associated with them are also provided. We show that some of the existing methods for MPCC reach AC-stationary points, extending previous convergence results. In particular, the new results include the linear case, not previously covered. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• 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