Firstly, we establish continuity and closedness of second-order contingent derivatives and second-order adjacent derivatives for set-valued maps.
首先，我们建立了集值映射二阶相依导数和二阶邻接导数的连续性和闭性。
Then relative interior is introduced and an alternative theorem of generalized convex set-valued maps is established by using the separation theorem.
引进了相对内部，应用凸集分离定理建立了一个广义凸集值映射的择一性定理。
Under the nearly cone-subconvexlike set-valued maps, relations of strong efficient solutions and Kuhn-Tucker saddle point of set-valued optimization problem are dicussed.
集值优化问题的最优性条件与解集的结构理论在集值优化理论中占有重要的地位。
In Chapter 4, we introduce higher-order generalized contingent derivatives and higher-order generalized adjacent derivatives for set-valued maps, and discuss some of their properties.
在第四章里，引入集值映射的高阶广义相依导数和高阶广义邻接导数，同时讨论了它们的一些性质。
In chapter 2, we introduce the knowledge that the paper use, introducing these conception of cone, cone convex set-valued maps, tangent cones, and tangent derivatives of set-valued mapping, etc.
第二章是预备知识，介绍了锥、锥凸集值函数、切锥与集值映射的切导数等的相关知识。
The problem of the existence of a cone subdifferential for the cone convex set valued maps in the locally convex, linear and topological vector space is discussed.
在局部凸线性拓扑向量空间讨论了一种锥凸集值映射的锥次微分的存在性问题，证明了几个锥次微分的存在定理。
Then, a theorem of the alternative for generalized subconvexlike set valued maps in real linear spaces is established.
然后，在实线性空间中建立了一个广义次似凸集值映射的择一性定理。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
This paper extends the concept of arc connected convexness of single valued maps to set valued maps.
将单值映射的弧连通凸概念推广到了集值映射。
This paper extends the concept of arc connected convexness of single valued maps to set valued maps.
将单值映射的弧连通凸概念推广到了集值映射。
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