On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

Autor(es)

Haeser, Gabriel ^[1] ; Laura Schuverdt, Maria ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Math & Stat, Sao Paulo - Brazil

^[2] Univ La Plata, FCE, Dept Math, CONICET, RA-1900 La Plata, Buenos Aires - Argentina

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 149, n. 3, p. 528-539, JUN 2011.
• Citações Web of Science: 11

Resumo

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions. (AU)

• Processo FAPESP: 09/09414-7 - Métodos de penalidade e condições de otimalidade
• Beneficiário: Gabriel Haeser
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado