含参广义向量均衡问题有效解的稳定性

在不需要映射的单调性和解映射信息的条件下,本文讨论了一类含参广义向量均衡问题有效解映射的下半连续性和Hausdorff上半连续性.利用映射的严格C-凹性和C-似凸性,本文得到了该类含参广义向量均衡问题有效解映射的下半连续性.进一步,利用标量化方法,证明了该类含参广义向量均衡问题有效解映射的Hausdorff上半连续性.     

参数弱向量平衡问题解集映射的连续性

运用非线性标量化方法, 讨论参数弱向量平衡问题解集映射的上半连续性和下半连续性, 并举例说明了所得结果的正确性.     

约束锥扰动多目标规划锥有效解集的闭性和半连续性

本文研究拓扑向量空间中目标映射和约束映射均为连续,约束映射的约束锥为半连续的条件下,受扰动可达目标集的锥有效点集和锥弱有效点集的闭性、半连续性和锥半连续性.在此基础上,得到了约束锥扰动多目标规划问题的锥有效解集和锥弱有效解集的闭性和半连续性.     

扰动广义向量变分不等式解的半连续性

本文通过标量化的方法在Hausdorff拓扑向量空间中讨论了扰动广义向量变分不等式解的下半连续性.     

含参广义集值向量均衡问题有效解映射下半连续的最优条件

在实Hausdorff拓扑向量空间中研究一类含参广义集值向量均衡问题弱有效解与有效解映射的下半连续性. 在近似锥-次类凸的条件下, 运用标量化的方法得到弱有效解的标量化结果. 在适当条件下, 得到含参广义集值向量均衡问题弱有效解与有效解映射下半连续性定理.     

参数广义弱向量拟平衡问题解映射的H-连续性刻画

研究了Hausdorff拓扑向量空间中的一类参数广义弱向量拟平衡问题(PGWVQEP)的稳定性.首先，给出了此问题的参数间隙函数，研究了参数间隙函数的连续性.然后, 提出了一个与参数间隙函数相关的关键假设，讨论了它的连续性，并给出关键假设的等价刻画.最后， 借助于假设，获得了PGWVQEP解映射Hausdorff半连续的充分必要条件.并举例验证了所得结果.     

拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性

本文研究局部凸的Hausdorff拓扑向量空间中锥拟凸多目标规划锥有效解集的连通性问题。利用广义鞍点定理,证明了目标映射为一对一的锥拟凸多目标规划的锥有效解集是连通的。     

含参原始与对偶弱向量近似平衡问题的稳定性北大核心CSCD

借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.     

含参原始与对偶弱向量近似平衡问题的稳定性

借助于标量化技巧讨论了含参原始与对偶弱向量近似平衡问题的稳定性.首先,在邻近C-次似凸性假设下获得原始平衡问题近似解集的连通性和近似解集映射的Hausdorff上(下)半连续性.然后,利用标量化方法,在较弱假设下获得了含参对偶弱向量平衡问题近似解集的连通性及近似解集映射的Hausdorff连续性的充分性条件.最后,给出了在向量优化问题中的一个应用.所得结果推广和改进了已有文献中相应结论.     

对称集值向量拟均衡问题解集的稳定性

本文研究了对称集值向量拟均衡问题解集的稳定性.证明了在约束映射满足一定连续性与目标映射是锥-恰当拟凸的集值映射条件下,对称集值向量拟均衡问题的解集是稳定的,还证明了每个对称集值向量拟均衡问题的解集至少存在一个本质连通区.     

Well-posedness and stability in vector optimization problems using Henig proper efficiency

In this article, we study well-posedness and stability aspects for vector optimization in terms of minimizing sequences defined using the notion of Henig proper efficiency. We justify the importance of set convergence in the study of well-posedness of vector problems by establishing characterization of well-posedness in terms of upper Hausdorff convergence of a minimizing sequence of sets to the set of Henig proper efficient solutions. Under certain compactness assumptions, a convex vector optimization problem is shown to be well-posed. Finally, the stability of vector optimization is discussed by considering a perturbed problem with the objective function being continuous. By assuming the upper semicontinuity of certain set-valued maps associated with the perturbed problem, we establish the upper semicontinuity of the solution map.     

Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems

In this paper we establish sufficient conditions for the solution set of parametric multivalued vector quasiequilibrium problems to be semicontinuous. All kinds of semicontinuity are considered: lower semicontinuity, upper semicontinuity, Hausdorff upper semicontinuity and closedness. Moreover, we investigate both the “weak” and “strong” solutions of quasiequilibrium problems.     

Stability of weak vector variational inequality

In this paper, a key assumption is introduced by virtue of a parametric gap function. Then, by using the key assumption, sufficient conditions of the continuity and Hausdorff continuity of a solution set map for a parametric weak vector variational inequality are obtained in Banach spaces with the objective space being finite-dimensional.     

Semicontinuity of Solution Mappings to Parametric Generalized Vector Equilibrium Problems

In this article, stability results concerning the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mappings to parametric generalized vector equilibrium problems with neither the monotonicity of mappings nor any information of the solution mappings are established by using scalarization methods and a new density result.     

Upper semicontinuity of the solution maps in homogeneous vector quasi-equilibrium problems

The aim of this work was to study the solution maps in the vector homogeneous quasi-equilibrium problems. Here, we establish some sufficient and necessary conditions for upper semicontinuity of the solution maps in the vector homogeneous quasi-equilibrium problems. The results presented extend and improve the preceding results of Oetlli and Yen [Oetlli, W. and Yen, N.D., 1995, Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems. In: F. Giannessi and A. Maugeri (Eds) Variational Inequalities and Network Equilibrium Problems (New York: Plenum Press)].     

含参弱向量均衡问题的适定性

在实Hausdorff拓扑线性空间中研究了含参弱向量均衡问题的适定性.证明了在适当条件下由近似网定义的含参适定性等价于近似解映射的上半连续性,并给出了所研究问题各种适定的充分性条件.     

Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.     

Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities

We consider five different types of systems of generalized vector variational inequalities and derive relationships among them. We introduce the concept of pseudomonotonicity for a family of multivalued maps and prove the existence of weak solutions of these problems under these pseudomonotonicity assumptions in the setting of Hausdorff topological vector spaces as well as real Banach spaces. We also establish the existence of a strong solution of our problems under lower semicontinuity for a family of multivalued maps involved in the formulation of the problems. By using a nonlinear scalar function, we introduce gap functions for our problems by which we can solve systems of generalized vector variational inequalities using optimization techniques. The first two authors were supported by SABIC and Fast Track Research Grants SAB-2006-05. They are grateful to the Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia for providing excellent research facilities.     

Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems

We discuss the lower semicontinuity of the set of efficient solutions for parametric generalized systems with monotone bifunctions in real locally convex Hausdorff topological vector spaces. This research was partially supported by the National Natural Science Foundation of China (10561007), the Natural Science Foundation of Jiangxi Province, China, and a grant from the National Science Council of ROC.