锥似凸映射下集值优化Henig有效解的高阶最优性条件(英文)

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.     

Second-Order Optimality Conditions for Set-Valued Vector Equilibrium Problems

In this article, by using the generalized second-order contingent (adjacent) epiderivatives of set-valued maps, we obtain necessary optimality conditions and sufficient optimality conditions for weakly efficient solutions, Henig efficient solutions to the set-valued vector equilibrium problems with constraints. Some results of this article improve the corresponding results in literatures by lessening the assumption of convexity.     

Higher order optimality conditions for Henig efficient solutions in set-valued optimization

In this paper, higher order generalized contingent epiderivative and higher order generalized adjacent epiderivative of set-valued maps are introduced. Necessary and sufficient conditions for Henig efficient solutions to a constrained set-valued optimization problem are given by employing the higher order generalized epiderivatives.     

Higher-Order Optimality Conditions for Set-Valued Optimization

This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map.     

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.     

Generalized Constraint Qualifications and Optimality Conditions for Set-Valued Optimization Problems

In this paper we discuss the connections of four generalized constraint qualifications for set-valued vector optimization problems with constraints. Then some K-T type necessary and sufficient optimality conditions are derived, in terms of the contingent epiderivatives.     

集值优化问题Benson真有效解的高阶Fritz John型最优性条件

本文讨论的是集值优化问题Benson真有效解的高阶Fritz John型最优性条件,利用Aubin和Fraukowska引入的高阶切集和凸集分离定理,在锥-似凸映射的假设条件下,获得了带广义不等式约束的集值优化问题Benson真有效解的高阶Fritz John型必要和充分性条件.     

集值优化问题严最大有效解的高阶刻画

在实赋范线性空间中考虑集值优化问题的严有效性.利用高阶导数的性质给出了受约束于固定集的集值优化问题取得严最大有效解的高阶导数型最优性必要条件.当目标函数为锥凹集值映射时,利用严最大有效点的性质得到集值优化问题取得严最大有效解的充分条件.     

Higher-Order Variational Sets and Higher-Order Optimality Conditions for Proper Efficiency in Set-Valued Nonsmooth Vector Optimization

Higher-order variational sets are proposed for set-valued mappings, which are shown to be more convenient than generalized derivatives in approximating mappings at a considered point. Both higher-order necessary and sufficient conditions for local Henig-proper efficiency, local strong Henig-proper efficiency and local λ-proper efficiency in set-valued nonsmooth vector optimization are established using these sets. The technique is simple and the results help to unify first and higher-order conditions. As consequences, recent existing results are derived. Examples are provided to show some advantages of our notions and results. This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

集值优化问题的高阶最优性条件(借助Studniarski导数)(英文)

本文研究的是约束集值优化问题的高价最优性条件.首先通过借助集值映射的Stud-niarski导数和严格局部有效性,讨论了集值优化问题的高阶必要条件和充分条件.对于充分条件,初始空间必须是有限维的.其次在初始空间和目标空间是有限维的以及集值映射是m阶稳定的条件下,也得到了此约束集值优化问题的高阶最优性条件.     

内部锥-凸集值映射Henig有效性的Morea-Rockafellar定理

本文利用集值映射弱次梯度的Morea-Rockafellar定理,在内部(锥)-凸性假设下,得到了集值映射关于Henig有效性的Morea-Rockafellar定理.其结论为:在内部(锥)-凸条件下,两个集值映射和的Henig有效次梯度可以表示成它们Henig有效次梯度的和.     

On Higher-Order Sensitivity Analysis of Parametric Henig Set-Valued Equilibrium Problems

Abstract

In the article, we discuss sensitivity analysis of a parametric Henig set-valued equilibrium problem. In detail, relationships between the higher-order contingent derivative of the solution map of this problem and those of objective and constraint maps are established. Finally, applications to parametric set-valued optimization problems are given.     

On Optimality Conditions for Henig Efficiency and Superefficiency in Vector Equilibrium Problems

Abstract

Necessary optimality conditions for local Henig efficient and superefficient solutions of vector equilibrium problems involving equality, inequality, and set constraints in Banach space with locally Lipschitz functions are established under a suitable constraint qualification via the Michel–Penot subdifferentials. With assumptions on generalized convexity, necessary conditions for Henig efficiency and superefficiency become sufficient ones. Some applications to vector variational inequalities and vector optimization problems are given as well.     

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.     

二层多目标规划的最优性条件

本文在集值优化的框架下提出了一个二层多目标规划模型（BLMOP）.利用集值映射的相依导数和相依上导数,给出了几个有关（BLMOP）的弱有效解的必要或充分最优性条件.     

Benson真有效解意义下集值优化问题的最优性条件

引进了集值映射关于锥的(1,α)-阶Clarke切导数,(1,α)-阶Adjacent切导数,(1,α)-阶Contingent切导数概念;应用它们导出了具Slater约束规格的集值优化问题的Benson真有效解的广义Kuhn-Tucker最优性条件．     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

Optimality Conditions for C1,1 Vector Optimization Problems

The main purpose of this paper is to make use of the second-order subdifferential of vector functions to establish necessary and sufficient optimality conditions for vector optimization problems.     

Optimality Conditions for Vector Equilibrium Problems in Terms of Contingent Epiderivatives

In this article, we study some important properties of contingent epiderivatives concerning steady functions and a cone with a compact base along with its applications to establish necessary and sufficient optimality conditions for weakly efficient, Henig efficient, globally efficient and superefficient solutions for no constraints and constraints (it concludes cone constraint, equality constraint and a constraint set) vector equilibrium problems in terms of contingent epiderivatives. We also give some examples to illustrate obtained results.     

集值映射的次微分以及最优性条件

基于已有的集值映射的弱次微分的概念,定义了集值映射的Henig全局次微分,研究了它的存在性条件以及运算性质．利用这一概念,分别给出了具约束向量集值最优化问题的Henig全局有效解对的必要性条件和充分性条件．