向量集值优化超有效解的对偶问题  

Duality in Vector Optimization of Set-valued Maps with Super Efficient Solutions

作　　者：盛宝怀[1] 周颂平[2] 刘三阳[3] 

机构地区：[1]绍兴文理学院数学系,绍兴312000 [2]浙江工程学院数学研究所,杭州310018 [3]西安电子科技大学应用数学系,西安710071

出　　处：《数学物理学报（A辑）》2004年第4期426-434,共9页Acta Mathematica Scientia

基　　金：浙江省自然科学基金(102002)国家自然科学基金(10371024)资助

摘　　要：借助于Contingent切锥和集值映射的上图而引入的有关集值映射的Contingent切导数, 对约束集值优化问题的超有效解建立了最优性Kuhn-Tucker必要及充分性条件,借此建立了 向量集值优化超有效解的Wolfe型和Mond-Weir型对偶定理.A generalized Kuhn-Tucker optimality condition of constrained vector optimization of set-valued maps with super efficiency is obtained with the help of the Contingent tangent derivatives which are developed with the aid of Contingent tangent cone and the epigraphy of the set-valued map, with which the weak duality theorems, direct duality theorems and the converse theorems for Wolfe type and Mond-Weir type duality are established.

关 键 词：Contingent切锥 集值映射 对偶 

分 类 号：O221.6[理学—运筹学与控制论]