一类向量极值问题的最优性条件

本文利用序线性空间中关于次似凸集值映射的择一性定理,得出了具有广义等式和不等式约束的向量极值问题的最优性条件.     

集值优化导数型最优性条件

借助于相依上导数的概念,建立了锥次类凸集值映射的导数型择一性定理,并利用择一性定理获得了集值优化导数型的最优性必要条件和充分条件.     

广义次似凸集值优化的鞍点定理

讨论广义次似凸集值优化的鞍点定理.给出广义次似凸集值映射的两个性质.定义广义次似凸集值优化的Fritz-John鞍点和Kuhn-Tucker鞍点.获得一系列广义次似凸集值优化的鞍点定理.     

Optimality conditions of set-valued optimization problem involving relative algebraic interior in ordered linear spaces

In this article, firstly, a generalized cone subconvexlike set-valued map involving the relative algebraic interior is introduced in ordered linear spaces. Secondly, some properties of a generalized cone subconvexlike set-valued map are investigated. Finally, the optimality conditions of set-valued optimization problem are established.     

广义次似凸集值优化的对偶定理

我们讨论了广义次似凸集值优化的对偶定理.首先,我们给出了广义次似凸集值优化的对偶问题.其次,我们给出了广义次似凸集值优化的对偶定理.最后,我们考虑了广义次似凸集值优化问题的标量化对偶,并给出了一系列对偶定理.     

序线性空间中向量极值问题的最优性条件

本文在序线性空间中建立了广义次似凸映射下的择一定理,运用此定理,得出一类向量极值问题的最优性条件.     

Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps

In the framework of locally convex topological vector spaces, we establish a scalarization theorem, a Lagrange multiplier theorem and duality theorems for superefficiency in vector optimization involving nearly subconvexlike set-valued maps.     

ɛ-Subdifferentials of Set-valued Maps and ɛ-Weak Pareto Optimality for Multiobjective Optimization

In this paper we consider vector optimization problems where objective and constraints are set-valued maps. Optimality conditions in terms of Lagrange-multipliers for an ɛ-weak Pareto minimal point are established in the general case and in the case with nearly subconvexlike data. A comparison with existing results is also given. Our method used a special scalarization function, introduced in optimization by Hiriart-Urruty. Necessary and sufficient conditions for the existence of an ɛ-weak Pareto minimal point are obtained. The relation between the set of all ɛ-weak Pareto minimal points and the set of all weak Pareto minimal points is established. The ɛ-subdifferential formula of the sum of two convex functions is also extended to set-valued maps via well known results of scalar optimization. This result is applied to obtain the Karush–Kuhn–Tucker necessary conditions, for ɛ-weak Pareto minimal points     

关于一类向量极值问题弱有效解的充分必要条件

本文研究带集合约束的向量极值问题。运用局部凸Hausdorff拓扑向量空间中广义次似凸映射的择一定理和其他一些结论，得到了关于集合约束向量极值问题弱有效解的几个充分必要条件．     

Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems

This paper gives several characterizations of nearly subconvexlike set-valued maps (see Ref. 1) and shows that a weakly efficient solution and a Benson properly efficient solution of a vector optimization problem with nearly-subconvexlike objectives and constraints can be expressed in terms of saddle points defined in a suitable sense.