ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY  

作　　者：盛宝怀 刘三阳 

机构地区：[1]Departmem of Applied Mathematics,Xidian University,Xi''an 710071,P R China [2]Institute of Mathematics,Ningbo University,Ningbo,Zhejiang 315211,P R China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2002年第12期1444-1451,共8页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina ( 69972 0 3 6);theDoctorFoundationofNingboCity

摘　　要：A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.

关 键 词：contingent tangent cone set-valued map Benson proper efficiency Fritz John condition 

分 类 号：O211.6[理学—概率论与数理统计]