A relaxed constant positive linear dependence constraint qualification and applications

Autor(es)

Andreani, Roberto ^[1] ; Haeser, Gabriel ^[2] ; Laura Schuverdt, Maria ^[3] ; Silva, Paulo J. S. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Math Stat & Sci Comp, Dept Appl Math, Campinas, SP - Brazil

^[2] Univ Fed Sao Paulo, Inst Sci & Technol, Sao Jose Dos Campos, SP - Brazil

^[3] Univ La Plata, FCE, Dept Math, CONICET, RA-1900 La Plata, Bs As - Argentina

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

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATICAL PROGRAMMING; v. 135, n. 1-2, p. 255-273, OCT 2012.
• Citações Web of Science: 58

Resumo

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ. (AU)

• Processo FAPESP: 06/53768-0 - Métodos computacionais de otimização
• Beneficiário: José Mário Martinez Perez
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 09/09414-7 - Métodos de penalidade e condições de otimalidade
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado