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熊昀暄 《数学的实践与认识》2016,(3):254-258
研究了具有控制结构的集值强向量均衡问题.通过Ky Fan截口定理得到了具有控制结构的集值强向量均衡问题解的存在性定理.并在映射满足一定条件的基础上,得到了集值强向量均衡问题所构成的空间M中,大多数(在Baire分类意义下)强向量均衡问题解集是稳定的. 相似文献
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利用比较弱的锥连续性与著名的Fan-KKM定理,得到一类具有控制结构的强向量均衡问题的解,并讨论其解集的性质,改进了相关文献的主要研究结果. 相似文献
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提出一类新的广义向量拟均衡问题,并得到解的存在性定理.用于证明向量变分不等式和向量优化问题的解的存在性. 相似文献
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研究锥伪单调、锥拟凸和上锥连续映射在某种强制性条件下的向量均衡问题解集的特征,建立强制性条件与向量均衡问题解集的关系,得到对偶向量均衡问题局部解集含于向量均衡问题解集的性质和向量均衡问题解集的非空性条件,给出在锥伪单调、锥拟凸和上锥连续映射条件下向量均衡问题解集的非空有界性与强制性条件的等价性. 相似文献
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研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理. 相似文献
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考虑一类隐式形式多值向量均衡问题的解的存在性,该类问题包含了多值均衡问题、隐式向量均衡问题、多值变分不等式问题、向量变分不等式问题以及向量互补问题作为其特殊情形.利用广义Fan-Browder不动点定理,得到了拓扑向量空间中该类问题解的存要性定理,该结果推广并统一了已有问题解的存在性结果. 相似文献
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在拓扑向量空间中,利用Ky Fan截口定理得到一个锥凸向量拟均衡问题弱Pareto解的存在性结果.作为该结果的应用,得到了一个对称向量拟均衡问题在支付映射为锥凸条件下弱Pareto解的存在性定理.该定理在较弱的条件下回答了Fu在文献[1]中提出的第二个问题,即在支付映射为锥凸且连续的条件下对称向量拟均衡问题的弱Pareto解是否存在.最后在赋范线性空间中研究了锥凸对称向量拟均衡问题弱Pareto解集的通有稳定性. 相似文献
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In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan’s main results are corrected. 相似文献
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In this paper, an iterative algorithm for solving the strong vector equilibrium problem with variable domination structure (VSVEP) is considered. First, an auxiliary problem for the VSVEP is introduced and the relationships between the auxiliary problem and VSVEP are discussed. Then, using the auxiliary principle technique, a projection iterative algorithm to compute the approximate solutions of the VSVEP is proposed and analysed. Furthermore, convergence of the iterative sequences generated by this algorithm is investigated under suitable conditions of continuity and convexity. These results extend and improve some recent works in this field. 相似文献
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A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems 总被引:1,自引:0,他引:1
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization
problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function
for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear
scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions
for generalized quasi-vector equilibrium problems.
This paper is dedicated to Professor Franco Giannessi for his 68th birthday 相似文献
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In this paper, two types of Levitin–Polyak well-posedness of vector equilibrium problems with variable domination structures
are investigated. Criteria and characterizations for two types of Levitin–Polyak well-posedness of vector equilibrium problems
are shown. Moreover, by virtue of a gap function for vector equilibrium problems, the equivalent relations between the Levitin–Polyak
well-posedness for an optimization problem and the Levitin–Polyak well-posedness for a vector equilibrium problem are obtained.
This research was partially supported by the National Natural Science Foundation of China (Grant number: 60574073) and Natural
Science Foundation Project of CQ CSTC (Grant number: 2007BB6117). 相似文献
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Harold P Benson 《Journal of Mathematical Analysis and Applications》1983,93(1):273-289
Vector maximization problems arise when more than one objective function is to be maximized over a given feasibility region. The concepts of efficiency and proper efficiency have played a useful role in the analysis of such problems. Recently these concepts have been extended to vector maximization problems in which the underlying domination cone is a convex cone. In this paper, efficient and properly efficient solutions for the vector maximization problem in which the underlying domination cone is any nontrivial, closed convex cone are examined. Differences between properly and improperly efficient solutions are established. Characterizations of efficient and properly efficient solutions are presented, and conditions under which efficient solutions exist and fail to exist are derived. 相似文献
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The aim of this paper is applying the scalarization technique to study some properties of the vector optimization problems
under variable domination structure. We first introduce a nonlinear scalarization function of the vector-valued map and then
study the relationships between the vector optimization problems under variable domination structure and its scalarized optimization
problems. Moreover, we give the notions of DH-well-posedness and B-well-posedness under variable domination structure and
prove that there exists a class of scalar problems whose well-posedness properties are equivalent to that of the original
vector optimization problem. 相似文献
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In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient
solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of
the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium
problem are proved in locally convex spaces. 相似文献
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Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented. 相似文献
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A method of duality for a mixed vector equilibrium problem 总被引:1,自引:0,他引:1
In this paper, a dual scheme for a mixed vector equilibrium problem is introduced by using the method of Fenchel conjugate
function. Under the stabilization condition, the relationships between the solutions of mixed vector equilibrium problem (MVEP)
and dual mixed vector equilibrium problem (DMVEP) are discussed. Moreover, under the same condition, the solutions of MVEP
and DMVEP are proved relating to the saddle points of an associated Lagrangian mapping. As applications, this dual scheme
is applied to vector convex optimization and vector variational inequality. 相似文献
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主要研究平衡问题解的存在性.通过对目标函数和可行集合的渐近分析,给出拟单调平衡问题解集非空的条件.进而用类似的方法研究了向量平衡问题解存在的条件,并将其应用到向量优化问题上. 相似文献