集值映射向量优化的Benson真有效性

BENSON PROPER EFFICIENCY IN VECTOR OPTIMIZATION WITH SET-VALUED MAPS

本文首先将单值映射的锥次类凸概念推广到集值映射，并对锥次类凸集值映射给出几个等价刻划和一个择一性定理．然后，利用这些概念与结果来研究拓扑线性空间中带集值映射的向量优化问题的Benson真有效性，获得两个标量化结果和两个Lagrange乘子定理．在定义了一个适当的集值Lagrange映射并对其引入真鞍点的概念之后，又建立了Benson真有效性的一个充分条件和一个充要条件最后还讨论了两个对偶问题．

in this paper, we first extend the concept of cone-subconvexlikeness of singlevalued maps to set-valued maps and present several equivalent characterizations and analternative theorem for cone-subconvexlike set-valued maps. The concept and these resultsare then applied to study Benson proper efficiency for a vector optimization problem withset-valued maps in topological vector spaces. Two scalarization results and two Lagrangemultiplier theorems are established. After introducing the new concept of a proper saddlepoint for an appropriate set-valued Lagrange map, we use it to provide a sufficient conditionand a necessary and sufficient condition for Benson proper efficiency. Two dual problemsare also discussed.