集值优化问题在有效意义下的最优性条件(英文)  

The Optimality Conditions of Set-valued Optimization Problems in the Sense of Efficiency

作　　者：侯震梅[1] 刘三阳[1] 周勇[1] 

机构地区：[1]西安电子科技大学应用数学系,西安710071

出　　处：《运筹学学报》2005年第3期24-30,共7页Operations Research Transactions

基　　金：This rersearch was supported by the national Science Foundation (Project:69972036)

摘　　要：本文在赋范空间中,讨论集值优化问题的有效元导数型最优性条件.当目标映射和约束映射的下方向导数存在时,在近似锥次类凸假设下利用有效点的性质和凸集分离定理得到了集值优化问题有效元导数型Kuhn-Tucker必要条件,在可微Γ-拟凸性的假设下得到了Kuhn-Tucker最优性充分条件;此外利用集值映射沿弱方向锥的导数的特性给出了有效解最优性的另一种刻画。In this paper, the optimality conditions of set-valued optimization problems with derivatives are established under efficiency in normed linear space. When the lower direct derivatives of objectives maps and constrained maps exist, under the assumption of nearly cone-subconvexlikeness, by using properties of set of efficient points and a separation theorem for convex sets, Kuhn-Tucker necessary conditions are obtained for set-valued optiKuhn-Tucker sufficient condition is obtained for set-valued optimization problems in sense of efficiency; moreover, anther characterization of optimality condition for efficiency is presented by using the properties of lower direct derivative of set-valued maps at weak feasible directs.

关 键 词：运筹学 集值优化 最优性条件 有效元 下方向导数 最优性条件 集值映射 优化问题 Kuhn-Tucker 最优性充分条件 凸集分离定理 赋范空间 必要条件 

分 类 号：O224[理学—运筹学与控制论] O221.2[理学—数学]