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.
出处
《应用数学学报》
CSCD
北大核心
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
关键词
ε严有效元
近似锥-次类凸
二元集值函数
εstrictly emcient element
near cone-subconvexlikeness
binary set-valued function
