Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization
Optimality Conditions for Strictly Efficient Solutions in Set-valued Optimization
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DOI：
10.1007/s10255-020-0971-y
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发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
Yihong Xu
中科院分区：
文献类型：
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作者：
Yihong Xu
利用修正的Dubovitskij-Miljutin锥，给出了集值函数的一种新的切导数M-导数.引入了几种广义伪凸集值函数。当目标函数和约束函数均为M-可导函数时，在近似锥次类凸的假设下，利用严格有效点集的性质和凸集分离定理，得到了集值优化问题中点对为严格有效元的Fritz John和Kuhn-Tucker最优性必要条件.在广义伪凸性的假设下，得到了集值优化问题的点对为严有效元的Kuhn-Tucker最优性充分条件.
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 areM-derivative, under the assumption of near conesubconvexlikeness, 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.