Saddle point and second order optimality in nondifferentiable nonlinear abstract multiobjective optimization

• Autor(a) principal: Santos,L.B. dos
• Data de Publicação: 2012
• Outros Autores: Rojas-Medar,M.A., Oliveira,V.A. de
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512012000200008
• topic: Multiobjetive optimization; abstract optimization problems; nonlinear programming; saddle point conditions; generalized second order conditions; generalized convexity

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789-809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.