近似锥-次类凸集值优化问题严有效解的广义鞍点刻画

Generalized Saddle Point Characterization of Strictly Efficient Solutions in Nearly Cone-subconvexlike Set-valued Optimization Problems

本文研究集值优化问题严有效解的广义鞍点刻画问题。利用广义鞍点的性质和凸集分离定理,得到了广义鞍点的一个集分离性质,并且在近似锥-次类凸假设下建立了集值优化问题严有效解为广义鞍点的充分条件和必要条件。

This paper studies the characterization of strict efficient solutions in set-valued optimization by generalized saddle. By using the properties of generalized saddle points and a separation theorem, a property of generalized saddle points is proved with set separation. Moreover, under the assumption of nearly cone-subconvexlikeness, the necessary and sufficient conditions for a strictly efficient solution being a generalized saddle point in set-valued optimization problems with maps are obtained.