非凸多目标主从向量集值优化锥有效解的最优性条件

The optimality conditions for nonconvex vector top base optimization of set valued maps

运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理 .引入向量优化弱Benson真有效元的概念 ,对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足La grange乘子型的必要及充分条件 ,并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件 .

A theorem of the alternative for the generalized subconvexlike set valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top base constrained optimization of set valued maps with the Benson proper efficiency are obtained.