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 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.

在改进的Dubovitskij-Miljutin锥的帮助下，引入了一种用于集值函数的新型切线导数M导数。介绍了几个广义伪凸集值函数。当目标函数和约束函数均为M时-导数，在近似圆锥子凸相似性的假设下，通过应用严格有效点集的性质和凸集的分离定理，弗里茨·约翰（Fritz John）和库恩·塔克（Kuhn-Tucker）获得了点对成为严格有效点元素的必要最优性条件集值优化问题。在广义伪凸的假设下，获得了一个Kuhn-Tucker充分的最优条件，该条件使得点对成为集值优化问题的严格有效元素。