集值优化问题严有效解的高阶标量化定理  

Higher-Order Scalarization Theorems for Strictly Efficient Solutions of Set-Valued Optimization Problems

作　　者：贺丽娟[1,2] 王其林[2] 

机构地区：[1]西南财经大学工商管理学院,成都611130 [2]重庆交通大学理学院,重庆400074

出　　处：《应用泛函分析学报》2012年第4期395-399,共5页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11171362;11071267);重庆市自然科学基金(cstc2011jjA00013);重庆交通大学高教所教改研究课题(1003011)

摘　　要：讨论了集值优化问题严有效解的高阶导数型标量化定理.首先得到了集值优化问题严有效解的一个高阶导数型必要性条件,其次获得了集值优化问题严有效解的标量化必要性条件和充分性条件.In this paper,higher-order derivatives type scalarization theorems are discussed for strictly efficient solutions of set-valued optimization problems.Firstly,we obtain a generalized higherorder derivatives type necessary optimality condition for strictly efficient solutions of a set-valued optimization problem.Secondly,scalarization necessary conditions and sufficient conditions are derived for strictly efficient solutions of set-valued optimization problems by employing generalized higher-order epiderivatives.

关 键 词：集值优化问题 广义高阶上图导数 严有效解 标量化 

分 类 号：O224[理学—运筹学与控制论]