CONVERGENCE PROPERTIES OF A SECOND ORDER AUGMENTED LAGRANGIAN METHOD FOR MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

Autor(es)

Andreani, Roberto ^[1] ; Secchin, Leonardo D. ^[2] ; Silva, Paulo J. S. ^[1]

Afiliação do(s) autor(es)

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

^[2] Univ Fed Espirito Santo, Dept Appl Math, Sao Mateus, ES - England

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON OPTIMIZATION; v. 28, n. 3, p. 2574-2600, 2018.
• Citações Web of Science: 3

Resumo

Mathematical programs with complementarity constraints (MPCCs) are difficult optimization problems that do not satisfy the majority of the usual constraint qualifications (CQs) for standard nonlinear optimization. Despite this fact, classical methods behave well when applied to MPCCs. Recently, Izmailov, Solodov, and Uskov proved that first order augmented Lagrangian methods, under a natural adaption of the linear independence constraint qualification to the MPCC setting (MPCC-LICQ), converge to strongly stationary (S-stationary) points, if the multiplier sequence is bounded. If the multiplier sequence is not bounded, only Clarke stationary (C-stationary) points are recovered. In this paper we improve this result in two ways. For the case of bounded multipliers we are able replace the MPCC-LICQ assumption by the much weaker MPCC-relaxed positive linear dependence condition (MPCC-RCLPD). For the case with unbounded multipliers, building upon results from Scholtes, Anitescu, and others, we show that a second order augmented Lagrangian method converges to points that are at least Mordukhovich stationary (M-stationary) but we still need the more stringent MPCC-LICQ assumption. Numerical tests, validating the theory, are also presented. (AU)

• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs