On First Order Optimality Conditions for Vector Optimization  

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

机构地区：[1]Programa de Engenharia de Sistemas de Computacao,COPPE-UFRJ,CP 68511,Rio de Janeiro-RJ,21945970,Brazil,Instituto de Matematica Pura e Aplicada (IMPA), Estrada Dona Castorina 110,Rio de Janeiro,RJ,CEP 22460-320,Brazil,Instituto de Matematica Pura e Aplicada (IMPA),Estrada Dona Castorina 110,Rio de Janeiro,RJ,CEP 22460-320,Brazil

出　　处：《Acta Mathematicae Applicatae Sinica》2003年第3期371-386,共16页应用数学学报（英文版）

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)

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.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.

关 键 词：Cone constraints vector optimization Pareto minimization first order optimality conditions convex programming DUALITY 

分 类 号：O224[理学—运筹学与控制论]