线性空间中集值映射向量最优化的最优性条件

Optimality Conditions for Vector Optimization of Set-valued Maps

李泽民建立了实线性空间中次似凸集值映射向量最优化问题的K T条件和Lagrange乘子定理。笔者首先引进了广义次似凸集值映射的概念。然后 ,在实线性空间中建立了一个广义次似凸集值映射的择一性定理。最后 ,利用择一性定理 。

Kuhn Tucker optimality conditions and Lagrange multipliers for vector optimization problems with subconvexlike set valued maps wereestablished by Li zemin. Firstly, the concept of generalized subconvexlikeness for set valued maps is introduced in this paper. Then, a theorem of the alternative for generalized subconvexlike set valued maps in real linear spaces is established. Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.