Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization

• 作者: Yi-hong XU
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 891-901
• 页数: 11页
• 语种: 英文

摘要

A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the objective function and constraint function are M-derivative,under the assumption of near cone-subconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem.Under the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.