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1.
朱元国 《应用数学》1998,11(4):20-23
本文先讨论了一个KyFan截口定理的随机化形式,然后利用它讨论了一个隐式随机向量值变分不等式和一个显式随机向量值变分不等式的随机解的存在性.  相似文献   

2.
关于一类随机变分不等式和随机拟变分不等式问题   总被引:1,自引:0,他引:1  
本文对单值和多值情形的随机变分不等式和随机拟变分不等式得出可测解的存在性条件。另外还利用KKM-技巧及著名的Ky Fan定理对一类确定型的广义拟变分不等式讨论了解的存在性问题。本文的结果改进和发展了[10,11,12]中的重要结果。  相似文献   

3.
随机内积模上的变分不等式   总被引:1,自引:0,他引:1  
罗群 《数学研究》1997,30(1):72-77,96
给出随机内积模上变分不等式的解的存在性定理.这些结果有利于进一步研究随机内积极模上变分不等式、拟变分不等式和相补问题.  相似文献   

4.
多用户多准则随机系统最优与最优收费   总被引:1,自引:0,他引:1  
针对固定交通需求量和出行者的时间价值为离散分布的多准则随机交通均衡,分别研究了依费用度量和依时间度量的多用户多准则随机系统最优和最优收费问题.分别建立了基于费用和基于时间的随机系统最优的最优化模型,阐述了该模型解的唯一性条件及等价的变分不等式问题.运用变分不等式方法,研究了一阶最优收费的可行性,即能否依边际定价原则,通过收取与出行者类别无关的道路收费使多用户多准则随机均衡流与随机系统最优流一致.一阶最优收费不适用于依时间度量的随机系统最优情况,因而建立了一个最优化模型来得到此时的非歧视性道路收费.最后给出了具体算例.  相似文献   

5.
研究了一类非线性随机种群系统动力学模型的最优生育率控制问题.在加入外部随机因素扰动下,系统模型将会更具有实际意义.针对随机种群系统生育率控制问题,应用It?o公式,相应的伴随方程和变分不等式等经典理论,获得了随机种群系统最优生育率控制所满足的必要条件及其最优性组(由积分-偏微分方程和变分不等式组成).文中得到的结论是确定性种群系统的扩展,对随机控制理论具有现实的应用价值.  相似文献   

6.
建立了随机需求下直销多商品流供应链网络均衡模型,导出了供应链网络达到均衡的条件,它等价于一个有限维变分不等式.通过构建修改拟牛顿法,获得了随机需求下直销多商品流供应链网络均衡模型的解(变分不等式的解),并给出了1个算例,验证了模型的正确性和算法的可行性.  相似文献   

7.
使用辅助原理技巧研究了一类广义集值强非线性混合变分不等式.证明了此类集值强非线性混合变分不等式辅助问题解的存在性和唯一性;构建了一个新的三步迭代算法,通过辅助原理技巧,构建并计算此类非线性混合变分不等式的近似解,进一步证明非线性混合变分不等式解的存在性以及由算法产生的三个序列的收敛性.所得结论推广了近年来许多混合变分不等式和准变分不等式以及他们的有关结果.  相似文献   

8.
在本文中,我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组,通过用度量投影的方法,我们证明了这类广义变分不等式组解的存在性和唯一性.我们也建立了一类新的算法来逼近这一不等式组的解,本文的结果使得近期相关结果成为本文的特殊情况.  相似文献   

9.
本文在Banach空间中对变分不等式的例外簇,严格可行性及解的存在性三者之间的关系进行了研究,将补问题中的相应结果进行了推广.首先通过定义一类新的例外簇,在映射为拟单调的情况下,证明了变分不等式解的存在性与例外簇之间的关系,即若变分不等式不存在例外簇,则解一定存在.其次主要证明了变分不等式的严格可行性与例外簇之间的关系,即若变分不等式存在严格可行性,则例外簇不存在.  相似文献   

10.
在Vasicek利率模型的假设下,应用变分不等式方法分析了美式利率期权自由边界的性质.首先我们得到美式利率期权自由边界的下界,然后把自由边界问题化为变分不等式,通过引入惩罚函数证明了该变分不等式解的存在唯一性,最后证明了自由边界的单调性、有界性和C∞光滑性.  相似文献   

11.
In this paper, we introduce a system of vector equilibrium problems andprove the existence of a solution. As an application, we derive someexistence results for the system of vector variational inequalities. We alsoestablish some existence results for the system of vector optimizationproblems, which includes the Nash equilibrium problem as a special case.  相似文献   

12.
In this paper, we first introduce the system of generalized implicit variational inequalities and prove the existence of its solution. Then we derive existence results for systems of generalized variational and variational like inequalities and system of variational inequalities. As applications, we establish some existence results for a solution to the system of optimization problems which includes the Nash equilibrium problem as a special case  相似文献   

13.
《Optimization》2012,61(5):1211-1218
In this paper, we consider a system of vector variational inequalities and a system of nonsmooth variational inequalities defined by means of Clarke directional derivative. We also consider the Nash equilibrium problem with vector pay-offs and its scalarized form. We present some relations among these systems and problems. The existence results for a solution of system of nonsmooth variational inequalities are given. As a consequence, we derive an existence result for a solution of Nash equilibrium problem with vector pay-offs.  相似文献   

14.
The system of generalized vector equilibrium problems with applications   总被引:8,自引:0,他引:8  
In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.  相似文献   

15.
In this paper, we deal with set-valued equilibrium problems under mild conditions of continuity and convexity on subsets recently introduced in the literature. We obtain that neither semicontinuity nor convexity are needed on the whole domain when solving set-valued and single-valued equilibrium problems. As applications, we derive some existence results for Browder variational inclusions, and we extend the well-known Berge maximum theorem in order to obtain two versions of Kakutani and Schauder fixed point theorems.  相似文献   

16.
This paper is focused on the study of a dynamic competitive equilibrium by using Lagrangean multipliers. This mathematical formulation allows us the improve the Walrasian model by considering the common possibility of an uncharged delayed payment in a given time (for example, by using a credit card). Firstly the economic equilibrium problem is reformulated as an evolutionary variational problem; then the Lagrangean theory in infinite dimensional spaces is applied. Thanks to the application of this theory we obtain the existence of Lagrangean multipliers, which allows us to give a computational procedure for the equilibrium solutions.  相似文献   

17.
By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the ob jective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of complete metric spaces(Z,d), we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain XZ is countably compact in any Hausdorff topology weaker than that induced by d. When(Z, d) is a Féchet space(i.e., a complete metrizable locally convex space), our existence result only requires that the domain XZ is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems,which extend and improve the related known results.  相似文献   

18.
In this paper, we consider a unified framework of multiclass multicriteria mixed equilibrium, and the existence of uniform link tolls supporting such a mixed equilibrium as a system optimum. The network users are divided into different classes, and each class of traveler perceives his/her disutility associated with a route as a combination of two criteria given, respectively, by the travel time disutility and the time-irrelevant travel disutility. And users in a common class follow either user equilibrium (UE) principle or Cournot–Nash (CN) principle. A variational inequality model characterizing the multiclass multicriteria UE–CN mixed equilibrium behavior is developed. By utilizing the dual theory, we establish the existence of uniform link tolls supporting such mixed equilibrium as a system optimum.  相似文献   

19.
In this paper, we consider a lattice system of stochastic Zakharov equation with white noise. We first show that the solutions of the system determine a continuous random dynamical system with random absorbing set. And then we prove the random  asymptotic compact on the random absorbing set. Finally, we obtain the existence of a random attractor for the system.  相似文献   

20.
In this paper, we study the existence theorems of systems of variational inclusion problems. From these existence results, we study the existence theorems of systems of variational differential inclusion problems, mathematical program with systems of variational inclusion constraints, and mathematical program with systems of equilibrium constraints.  相似文献   

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