THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION  

作　　者：盛保怀 刘三阳 

出　　处：《Acta Mathematica Scientia》2002年第1期47-55,共9页数学物理学报（B辑英文版）

基　　金：the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)

摘　　要：The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.

关 键 词：set-valued derivative optimality condition pseudoconvex set-valued mapping 

分 类 号：O224[理学—运筹学与控制论]