集值优化问题在Henig真有效解意义下的导数型最优性条件

给出实的赋范空间中集值映射的Henig真有效解集的一些性质,并利用集值映射的相依上图导数和集值映射的次微分给出了集值优化问题Henig真有效解的最优性条件的充要条件.     

集值映射图的广义相依导数与真有效解的最优性条件

本文提出了集值映射图的SP-相依导数的概念,利用这个概念,给出了集值向量优化问题两种真有效解的最优性条件.     

超有效元意义下集值优化的最优性条件

该文在Hausdorff局部凸拓扑向量空间考虑约束集值优化问题(SOP)在超有效意义下的Fritz John条件和Kuhn-Tucker条件.首先借助集值映射的下半可微的概念给出这种空间中集值映射导数的定义, 据此讨论了超有效元的Fritz John最优性条件.最后, 给出约束集值优化问题(SOP)取得超有效元的充分条件.     

集值向量优化的二阶量优性条件

对集值映射引入了高阶Clarke导数,给出了判别集值向量优化所有效性的二阶Kuhn-Tucker条件,并且,借助于集值映射的强（弱）伪凸性给出了一个弱有效解的充分条件。     

集值映射的次微分的性质及其应用(英文)

本文讨论了文章"Subgradient of S-convex set-valued mappings and weak efficientsolutions"(Appl.Math.J.Chinese Univ.1998,13(4):463-472)中引入的集值映射的次微分的性质及应用.利用相依导数的性质,讨论次微分的性质,并得到了两个集值映射的和、复合以及交的次微分的运算法则.最后,通过这种次微分得到了集值优化问题最优性条件的充要条件,同时推广了此文中的定理7.     

伪凸集值映射的误差界

考虑了伪凸集值映射的误差界.证明了对于伪凸集值映射,局部误差界成立意味着整体误差界成立.通过相依导数,给出了伪凸集值映射存在误差界的一些等价叙述.     

集值优化问题在有效意义下的最优性条件

本文在赋范空间中,讨论集值优化问题的有效元导数型最优性条件.当目标映射和约束映射的下方向导数存在时,在近似锥次类凸假设下利用有效点的性质和凸集分离定理得到了集值优化问题有效元导数型Kuhn-Thcker必要条件,在可微Г-拟凸性的假设下得到了Kuhn-Tucker最优性充分条件;此外利用集值映射沿弱方向锥的导数的特性给出了有效解最优性的另一种刻画.     

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.     

二层多目标最优化问题解集的连通性

研究了二层多目标最优化模型(BLMOP)解集的连通性问题,其中(BLMOP)的上层集值目标函数由下层问题的有效点确定.把(BLMOP)看作成单层的集值函数优化问题,借助集值函数优化问题各种有效解集的连通性的结论,得到了(BLMOP)相应的有效解集连通性的结论.     

次预不变凸集值优化导数型最优性条件

引入了集值映射的α-阶锥次预不变凸概念,借助于α-阶相依上导数,建立了锥次预不变凸集值映射的导数型择—性定理,并利用择—性定理获得了集值优化导数型的最优性必要条件.     

拟不变凸集值优化的Kuhn-Tucker条件与Wolfe对偶

研究了拟不变凸集值优化最优性的Kuhn-Tucker条件及Wolfe型对偶问题．首先引进了alpha-阶G-拟不变凸集和alpha-阶S-拟不变凸集值函数的概念,由此研究了alpha-阶G-拟不变凸集所对应的伴随切锥及alpha-阶伴随导数的性质;最后,借助alpha-阶伴随切导数刻画了alpha-阶S-拟不变凸集值优化最优性的Kuhn-Tucker条件和Wolfe型对偶．     

Sensitivity and stability for the second-order contingent derivative of the proper perturbation map in vector optimization

Sensitivity analysis and stability analysis in vector optimization are dealt with in this paper. First, some relationships between the second-order contingent derivative of a set-valued map and its profile map are obtained. Secondly, the upper semicontinuity and lower semicontinuity of second-order contingent derivatives of set-valued maps are established. Finally, by virtue of the second-order contingent derivative of set-valued maps, quantitative information and qualitative information on the behavior of the proper perturbation map are obtained.     

Weak Subdifferential of Set-Valued Mappings

In this note we introduce a notion of the weak contingent generalized gradient for set-valued mappings associated with the contingent epiderivative of set-valued mappings introduced in "E. Bednarczuk and W. Song (1998). Contingent epiderivative and its applications to set-valued optimization. Control and Cybernetics, 27, 376-386; G.Y. Chen and J. Jahn (1998). Optimally conditions for set-valued optimization problems. Mathematical Methods of Operations Research, 48, 187-200." and prove that, under some additional condition, it coincides with the weak subdifferential introduced in "T. Tanino (1992). Conjugate duality in vector optimization. Journal of Mathematical Analysis and Applications, 167, 84-97." when the set-valued map is cone-convex. We also study the weak contingent generalized gradient of a sum of two set-valued mappings and optimality conditions for a set-valued vector optimization problem.     

Second-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization

In this paper, we propose the concept of a second-order composed contingent derivative for set-valued maps, discuss its relationship to the second-order contingent derivative and investigate some of its special properties. By virtue of the second-order composed contingent derivative, we extend the well-known Lagrange multiplier rule and the Kurcyusz–Robinson–Zowe regularity assumption to a constrained set-valued optimization problem in the second-order case. Simultaneously, we also establish some second-order Karush–Kuhn–Tucker necessary and sufficient optimality conditions for a set-valued optimization problem, whose feasible set is determined by a set-valued map, under a generalized second-order Kurcyusz–Robinson–Zowe regularity assumption.     

Variational characterization of the contingent epiderivative

In this paper the existence of the contingent epiderivative of a set-valued map is studied from a variational perspective. We give a variational characterization of the ideal minimal of a weakly compact set. As a consequence we characterize the existence of the contingent epiderivative in terms of an associated family of variational systems. When a set-valued map takes values in Rn we show that these systems can be formulated in terms of the contingent epiderivatives of scalar set-valued maps. By applying these results we extend some existing theorems.     

New second-order contingent epiderivatives and set-valued optimization problems

In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.     

Some results on sensitivity analysis in set-valued optimization

In the paper, the higher-order contingent derivative of a parametrized set-valued inclusion is first established. For its applications, we obtain sensitivity analysis of solution map in the decision variable space for a parametrized constrained set-valued optimization problem in terms of higher-order contingent derivatives.     

Optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps characterized by contingent epiderivative

In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.     

拟不变凸集值优化问题严有效解的最优性条件

在赋范线性空间中借助切导数研究集值优化问题的严有效性．当目标函数和约束函数相对于同一向量函数为拟不变凸时,利用凸集分离定理给出了集值优化问题取得严有效元的Kuhn—Xhcker型最优陛必要条件．利用切导数的性质,用构造性方法得到了拟不变凸集值优化问题取得严有效元的充分条件．