方向导数和广义锥-预不变凸集值优化问题  

Directional Derivatives and Generalized Cone-Preinvex Set-Valued Optimization

作　　者：余国林[1] 

机构地区：[1]北方民族大学信息与系统科学研究所,银川750021

出　　处：《数学学报（中文版）》2011年第5期875-880,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10901004);北方民族大学自主科研基金项目(2011)

摘　　要：讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件.This note deals with the optimality conditions of set-valued unconstraint optimization problems in topological vector spaces. Based upon the concepts of Dini directional derivatives and generalized eone-preinvexity for the set-valued mappings, the necessary and sufficient optimality conditions are established for weak and strong minimizer respectively in set-valued optimization problems.

关 键 词：集值优化 方向导数 广义锥-预不变凸集值映射 

分 类 号：O224[理学—运筹学与控制论]