An integro-differential parabolic variational inequality arising from the valuation of double barrier American option

This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem (i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality’ solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.     

纳什均衡问题解的特征

将纳什均衡问题转化为一个求解变分不等式问题 .在满足 nested $monotone^+$的条件下 ,给出求纳什均衡的思想 ,并对纳什均衡解的特征作了描述 .     

A general iterative method of fixed points for equilibrium problems and optimization problems

The purpose of this paper is to present a general iterative scheme as below:

A proximal point algorithm for a system of generalized mixed variational inequalities

This paper introduces and considers a new system of generalized mixed variational inequalities in a Hilbert space,which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases.By using the two concepts of 77-subdifferential andη-proximal mappings of a proper function,the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem.By applying the equivalence, a new and innovativeη-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed.The authors also study the convergence analysis of the new iterative method under much weaker conditions.The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.     

Stabilization of an Euler-Bernoulli beam with a tip mass under the unknown boundary external disturbances

This paper studies the stabilization problem of an Euler-Bernoulli beam with a tip mass, which undergoes unknown but uniform bounded disturbance at tip mass. Here the nonlinear feedback control law is used to cancel the effects of the external disturbances. For the controlled nonlinear system, the authors prove the well-posedness by the maximal monotone operator theory and the variational principle. Further the authors prove that the controlled nonlinear system is exponential stable by constructing a suitable Lyapunov function. Finally, some numerical simulations are given to support these results.     

STRONG CONVERGENCE OF MONOTONE HYBRID METHOD FOR FIXED POINT ITERATION PROCESSES*

K. Nakajo and W. Takahashi in 2003 proved the strong convergence theorems for nonex-pansive mappings, nonexpansive semigroups, and proximal point algorithm for zero point of monotone operators in Hilbert spaces by using the hybrid method in mathematical programming. The purpose of this paper is to modify the hybrid iteration method of K. Nakajo and W. Takahashi through the monotone hybrid method, and to prove strong convergence theorems. The convergence rate of iteration process of the monotone hybrid method is faster than that of the iteration process of the hybrid method of K. Nakajo and W. Takahashi. In the proofs in this article, Cauchy sequence method is used to avoid the use of the demiclosedness principle and Opial＇s condition.     

Henig globally efficiency for set-valued optimization and vector variational inequality

This paper deals with Henig globally efficiency in vector optimization involving generalized cone-preinvex set-valued mapping. Some properties of generalized cone-preinvex set-valued map are derived. It also disclose the closed relationships between Henig globally efficiency of generalized conepreinvex set-valued optimization problem and Henig globally efficiency of a kind of vector variational inequality.     

Continuity of solution mappings for parametric generalized set-valued weak vector equilibrium problems

This paper obtains some stability results for parametric generalized set-valued weak vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings, the authors establish the continuity of the solution mapping to a parametric generalized set-valued weak vector equilibrium problem without monotonicity. These results extend and improve some results in the literature. Some examples are given to illustrate the results.     

An Application of the Stability Theory in Constrained Nonlinear Optimization

1　 IntroductionIt is known that a given constrained nonlinear optimization problem can be transformedand solved by ordinary differential equations(ODE) [4,5] .Based on the preliminary resultsof [8～ 1 2 ] ,this paper uses a stability theory of ODE systems to analyze the asymptoticalproperties of differential equations which are derived from a given constrained nonlinearoptimization problem.We also state conditions of the overall uniform asymptoticalstability of the singular points aboutpart…     

相似关系的基本概念及其弱等价性质

本文的主要目的是确立相似关系的准确数学概念。首先本文将等价关系合理推广为弱等价关系,其次为解决描述部分与整体的共同属性问题,本文引入了向下相容性概念,并证明了向下相容性具有弱等价性质。然后用集合、子集、幂集、并集、１—１映射这五个最基本的概念及向下相容性公理、系统原理初步界定和刻划了相似关系、相似映射、相似要素、相似基、相似元（相似点）、相似系统这六个相似方面的基本概念。这对建立相似系统的分析具有重要意义。     

A POTENTIAL REDUCTION ALGORITHM FOR MONOTONE VARIATIONAL INEQUALITY PROBLEMS

1.IntroductionLetKbeanonemptyclosedconvexsubsetofR"andletF:R"-R"beacontinuousmapping.Avariationalinequalityproblem(VIP)istofindapointx*eKsuchthatThevariationalinequalityproblemmakesitswideappearanceinthestudyofvariousequilibriummodelsineconomics,oper...     

关于动态用户最优模型的几点分析

Ran等人(1996)构造了动态用户最优的变分不等式(VI)模型，并利用变分不等式问题与NLP之间的等价关系设计了松弛的优化算法。在深入分析Ran等(1996)的模型及求解算法的基础土，对其中的一些概念、理论推导以及算法过程进行了一定的改进。在此基础上，提出一个改进的动态用户最优(DUO)条件下的变分不等式(VI)模型。     

A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lvy Process with Terminal State Constraints

This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by L′evy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland's variational principle. Finally, the result is applied to the utility optimization problem in a financial market.     

Sample average approximation method for a class of stochastic variational inequality problems

This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu (2008), by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.     

基于网络分解与叠加的用户均衡网络敏感度分析

在交通网络用户均衡问题中,敏感度分析就是确定均衡网络状态时起讫点交通量及路段旅行时间的变化对路段交通量或路段旅 行费用的影响. 文章以确定型交通网络用户均衡问题为研究对象,推导了均衡网络的敏感度方程,运用网络分解与叠加的方法 提出了敏感度方程的求解方法,并分别给出了网络分解与叠加的实现方法. 该方法可以有效解决均衡网络敏感度分析中的秩亏 问题,相比基于数学规划法的敏感度分析有了很大改善. 这样,基于变分不等式的网络敏感度方程即可直接用于敏感度分析,为敏感度分析在交通规划、建设与管理中的应用提供了很大的便利.     

Allocating fixed costs with considering the return to scale: A DEA approach

When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis (DEA) researches have ignored the effect of the return to scale (RTS) in fixed cost allocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale (VRS) efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation. To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finally propose a fixed cost allocation approach in terms of principles as: (i) The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and (ii) the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.     

利用IC 卡数据估计公交OD 矩阵的模型及算法

利用公交IC卡数据建立了估计公交系统OD矩阵的双层数学规划模型,上层问题为广义最小二乘模型,下层问题为以变分不等式表示的基于超路径的公交网络均衡配流模型.采用启发式算法求解该双层数学规划模型,由于非对称性,运用了自适应的投影方法来求解下层的变分不等式问题,算例表明了模型的可行性和算法的有效性.     

极大熵准则下n人非合作条件博弈的期望Nash均衡

设每个局中人的纯策略空间都是实数集上的Borel集，在实数集上有m个确定的Lebesgue可测集，并存在从这n个纯策略空间的笛卡尔乘积到实数集的m个n元Borel函数。这m个Borel函数在对应Lebesgue可测集下的逆像构成这n个纯策略空间的笛卡尔乘积的一个划分，并且每n-1个纯策略空间的笛卡尔乘积都具有有限正Lebesgue测度。纯策略空间的笛卡尔乘积的不同分块中的纯局势一般具有不同的博弈结果。每个局中人的效用都是自己所选纯策略的一元函数。在极大熵准则是每个局中人的共同知识的条件下，我们得到了求这类博弈的期望意义下的Nash均衡点的方法．给出这种Nash均衡点的存在定理和可交换定理。最后给出一个应用例子。     

Introducing System Identification Strategy into Model Predictive Control

As system identification theory and model predictive control are belonged to two different research fields separately, so one gap exists between these two subjects. To alleviate this gap between them, one new idea proposed in this paper is to introduce system identification theory into model predictive control. As the most important element in model predictive control is the prediction of the output value for a nonlinear system, then the problem of deriving the prediction of the output value can be achieved by system identification theory. More specifically, a Bayesian approach is applied for the nonparametric estimation by modeling the prediction as realizations of zero mean random fields.Through comparing this kind of prediction corresponding to this Bayesian approach and the former direct weight optimization identification for nonlinear system, the authors see that if the unknown weights are chosen appropriately, these two approaches are equivalent to each other. Based on the obtained prediction of the output value, the authors substitute this prediction of the output value into one cost function of model predictive control, and then a quadratic programming problem with inequality constraints is formulated. When to solve this quadratic programming problem, a detailed process about how to derive its dual form is given. As the dual problem has a simple constraint set, it is amenable to the use of the common Gauss-Seidel algorithm, whose convergence can be shown easily.Finally, one simulation example confirms the proposed theoretical results.     

弹性需求用户平衡分配模型及其应用

对具有弹性需求的交通网络随机用户平衡分配问题进行了分析研究,将其描述为一个等价的变分不等式。最后将模型应用于拥护公交网络系统的平衡分配问题,并针对公交网络系统的特殊性,提出相应的求解算法 法。实例表明了模型的合理性和算法的有效性。