二元集值函数ε-严有效元的鞍点刻画  

Characterizations on ε-strictly Efficient Elements for Binary Set-valued Functions with Saddle Points

作　　者：徐义红[1] 张爱红[1] 

机构地区：[1]南昌大学数学系,南昌330031

出　　处：《应用数学学报》2016年第2期184-199,共16页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11461044);江西省自然科学基金(20151BAB201027);江西省教育厅科技(GJJ12010)资助项目

摘　　要：在Hausdorff局部凸拓扑线性空间中考虑二元集值函数ε-严有效鞍点问题,在近似锥-次类凸(凹)假设下,利用凸集分离定理得到二元集值函数取得ε-严有效元的松弛型鞍点的必要条件,利用标量化定理得到充分条件.特别地,当ε=0时得到二元集值函数取得严有效元的松弛型鞍点的充分必要条件.Abstract Some characterizations on ε-strictly efficient elements for binary set-valued functions with saddle points are considered in Hausdorff locally convex linear topological spaces. Under the hypothesis of near cone-subconvexlikeness （near cone-subconcavelikeness）, by applying separation theorem for convex sets, necessary optimality conditions of loose saddle points on c- strictly efficient elements for binary set-valued functions are established. Sufficient optimality conditions are also obtained with help of scalarization theorem. In particular, for ε= 0 the sufficient and necessary optimality conditions of loose saddle points on strictly efficient elements for binary set-valued functions are gained.

关 键 词：ε严有效元 近似锥-次类凸 二元集值函数 

分 类 号：O221.6[理学—运筹学与控制论]