On First Order Optimality Conditions for Vector Optimization

作     者：L.M.Gra■a Drummond A.N.Iusem B.F.Svaiter 

作者机构：Programa de Engenharia de Sistemas de ComputacaoCOPPE-UFRJCP 68511Rio de Janeiro-RJ21945970BrazilInstituto de Matematica Pura e Aplicada (IMPA) Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320BrazilInstituto de Matematica Pura e Aplicada (IMPA)Estrada Dona Castorina 110Rio de JaneiroRJCEP 22460-320Brazil 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2003年第19卷第3期

页      面：371-386页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：a post-doctoral fellowship within the Department of Mathematics of the University of Haifa and by FAPERJ (Grant No.E-26/152.107/1990-Bolsa) Partially supported by CNP_q (Grant No.301280/86).Partially supported by CNP_q (Grant No.3002748/2002-4) 

主　　题：Cone constraints vector optimization Pareto minimization first order optimality conditions convex programming duality 

摘      要：We develop first order optimality conditions for constrained vector optimization. The partial orders for the objective and the constraints are induced by closed and convex cones with nonempty interior. After presenting some well known existence results for these problems, based on a scalarization approach, we establish necessity of the optimality conditions under a Slater-like constraint qualification, and then sufficiency for the K-convex case. We present two alternative sets of optimality conditions, with the same properties in connection with necessity and sufficiency, but which are different with respect to the dimension of the spaces to which the dual multipliers belong. We introduce a duality scheme, with a point-to-set dual objective, for which strong duality holds. Some examples and open problems for future research are also presented.