集值映射向量优化问题的e-真有效解  

e-PROPER EFFICIENT SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH SET-VALUED MAPS

作　　者：彭建文[1] 杨新民[1] 

机构地区：[1]重庆师范学院数学与计算机科学系,重庆400047

出　　处：《高校应用数学学报（A辑）》2001年第4期486-492,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金 (1 9971 0 92;1 940 1 0 4 0 )

摘　　要：引入了集值映射向量优化问题的αe-弱有效解、e-真有效解、e-真鞍点概念 ,在近似广义 C-次似凸条件下 ,建立了 e-真有效解的标量化定理、Lagrange乘子定理和 e-真鞍点定理 ,并讨论了集值映射向量优化问题的αe-弱有效解的标量化定理和 Lagrange乘子定理 。The αe \|weak efficient solutions, e \|proper efficient solution, e \|proper saddle point for vector optimization problems with set\|valued maps(VP) are introduced.Under the assumption of the nearly generalized cone\|subconvexlikeness for set\|valued maps,the scalarization theorems,the Lagrange multipliers theorems for e \|proper efficient solution and the e \|proper saddle point theorems are established.The scalarization theorems,the Lagrange multipliers theorems for αe \|weak efficient solutions for (VP) are also obtained.These results generalize and improve the existing results.

关 键 词：集值映射 e-真有效解 e-真鞍点 近似广义C-次似凸 向量优化问题 标量化定理 LAGRANGE乘子定理 

分 类 号：O224[理学—运筹学与控制论]