可微向量极值问题的Benson真有效解的最优性条件

The Optimality Conditions of Benson Proper Efficient Solution for Differetiable Vector Extremum Problems

向量极值问题的Benson真有效解,是优化问题的一个最重要的方面,吸引了许多关注的目光.在序拓扑向量空间中,运用G-可微函数的性质和文献[1]中的定理4.1,获得了带集合约束的可微向量极值问题的Benson真有效解的几个最优性必要条件和充分条件.

Benson proper efficient solution for vector extremum problems is the most important aspect of optimization problems, and it has drawn lots of attention. In ordered topological vector spaces, by applying characterizations of G-differentiable function and Theorem 4.1 of Ref [ 1 ], several optimality necessary conditions and sufficient conditions of Benson proper efficient soluton for differentiable vector extremum problems with set constraint are obtained.