广义锥-凸集值优化问题Benson真有效元的最优性条件

Optimality Conditions on Benson Proper Efficient Element of Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps

该文讨论相依上图导数形式下广义锥-凸集值优化Benson真有效元的最优性条件。首先,借助相依上图导数建立了集值优化问题Benson真有效元的必要和充分最优性条件;其次,建立了具Slater约束规格的集值优化问题Benson真有效元的相依上图导数型Kuhn-Tucker充分最优性条件。

Under the assumption of generalized cone convex set-valued maps,the optimality conditions on Benson proper efficient element are discussed by using the contingent epiderivative.Firstly,the optimality necessary and sufficient conditions of the set-valued optimization problem in the sense of Benson proper efficiency is established.Secondly,Kuhn-Tucker type sufficient condition of the set-valued optimization problem in terms of contingent epiderivative is obtained.