实序线性空间中用广义二阶锥方向导数刻画集值优化ε-全局真有效解

在实序线性空间中,利用ε-全局真有效点的性质,借助广义二阶锥方向邻接(相依)导数的定义,建立了不受约束集值优化问题ε-全局真有效元的二阶必要最优性条件,同时得到了受约束集值优化问题在ε-全局真有效解意义下的二阶充分最优性条件.     

方向导数和广义锥-预不变凸集值优化问题

讨论拓扑向量空间中无约束集值优化问题的最优性条件问题.利用集值映射的Dini方向导数,在广义锥-预不变凸性条件下,建立了集值优化问题关于弱极小元和强极小元的最优性充分必要条件.     

用广义梯度刻画集值优化Benson真有效解

在锥偏序Banach空间中引入了一类关于集值映射的广义梯度，借助锥分离定理证明了广义梯度的存在性，由此崦给出集值向量优化Benson真有效解的特征。     

集值优化Benson真有效元的二阶刻画

引进了一种新的二阶组合切锥, 利用它引进了一种新的二阶组合切导数, 称为二阶组合径向切导数, 并讨论了它的性质及它与二阶组合切导数的关系, 借助二阶径向组合切导数, 分别建立了集值优化取得Benson真有效元的最优性充分和必要条件.     

集值优化问题强有效解的Kuhn Tucker最优性条件

在局部凸空间中考虑集值优化问题（VP）在强有效解意义下的Kuhn-Tucker最优性条件．在近似锥．次类凸假设下利用择一性定理得到了（VP）取得强有效解的必要条件，利用基泛函的性质给出了（VP）取得强有效解的充分条件，最后给出了一种与（VP）等价的无约束规划。     

近似锥一次类凸集值向量优化问题强有效解的广义鞍点刻画

本文研究了近似锥一次类凸集值向量优化强有效解的广义鞍点表示问题.利用择一定理,得到了近似锥-次类凸集值优化问题强有效解为广义鞍点的充分条件和必要条件.所得结果丰富了集值优化理论,并且拓广了广义鞍点的应用.     

一类不可微函数的二阶广义方向导数

本文研究一类不可微函数Ｃｈａｎｅｙ意义下的二阶广义方向导数,并得到这一类不可微问题的二阶最优性条件。     

广义函数的集值导数

本文应用广义函数的调和表示,引进了一维广义函数的集值导数,并给出了连续函数的集值导数的几种等价定义.局部Lipschitz函数的集值导数同Clarke定义的广义梯度一致;广义函数在一点附近是Lipschitz 函数之充要条件是它在该点的集值导数是有限的.当广义函数在某点的集值导数不同时包含+∞和-∞时,它的广义导函数在该点的某邻域上是Radon测度.利用一阶集值导数,给出了连续函数的逆函数存在定理;应用高阶集值导数,得到了广义函数取极值的两种非常一般的充分条件.广义函数在一个开区间上成为凸函数的充要条件是它在该区间内每点处的二阶集值导数都包含在[0,+∞]之中.于是,本文建立起一元非可微函数的一套令人满意的微分理论.     

非凸集值优化问题严有效解的强对偶定理

本文研究了非凸集值向量优化的严有效解在两种对偶模型的强对偶问题.利用Lagrange对偶和Mond-Weir对偶原理,获得了如下结果：原集值优化问题的严有效解,在一些条件下是对偶问题的强有效解,并且原问题和对偶问题的目标函数值相等;推广了集值优化对偶理论在锥-凸假设下的相应结果.     

锥方向高阶广义邻近导数及高阶Mond-Weir对偶(英文)

本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论.     

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and suffi-cient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set valued optimization.     

Second-order optimality conditions in set-valued optimization via asymptotic derivatives

In this article we give new second-order optimality conditions in set-valued optimization. We use the second-order asymptotic tangent cones to define second-order asymptotic derivatives and employ them to give the optimality conditions. We extend the well-known Dubovitskii–Milutin approach to set-valued optimization to express the optimality conditions given as an empty intersection of certain cones in the objective space. We also use some duality arguments to give new multiplier rules. By following the more commonly adopted direct approach, we also give optimality conditions in terms of a disjunction of certain cones in the image space. Several particular cases are discussed.     

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.     

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.     

Super efficient solutions for set-valued maps

Some properties for K-preinvex set-valued maps in terms of normal subdifferential are obtained. Furthermore, some sufficient conditions for existence of super minimal points and necessary optimality conditions for a general kind of super efficiency are established.     

Second-order contingent derivatives of set-valued mappings with application to set-valued optimization

In this paper, a family of parameterized set-valued optimization problems, whose constraint set depends on a parameter, are considered. Some calculus rules are obtained for calculating the second-order contingent derivatives of the composition and sum of two set-valued mappings. Then, by using these calculus rules, some results concerning second-order sensitivity analysis are established, and an explicit expression for the second-order contingent derivative of the (weak) perturbation mapping in the set-valued optimization problems is obtained.     

On super efficiency in set-valued optimization

The set-valued optimization problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of iccone-convexlikeness, by applying the seperation theorem, Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions, the necessary conditions are obtained for the set-valued optimization problem to attain its super efficient solutions. Also, the sufficient conditions for Kuhn-Tucker＇s, Lagrange＇s and saddle points optimality conditions are derived.     

Optimality conditions for proper efficient solutions of vector set-valued optimization

Based on the concept of an epiderivative for a set-valued map introduced in J. Nanchang Univ. 25 (2001) 122-130, in this paper, we present a few necessary and sufficient conditions for a Henig efficient solution, a globally proper efficient solution, a positive properly efficient solution, an f-efficient solution and a strongly efficient solution, respectively, to a vector set-valued optimization problem with constraints.