变分不等式

In this paper, we propose a simple alternating direction method.

本文提出了一个解线性变分不等式的简单的交替方向法。

In this thesis, we discuss some algorithms for giving the zeros of maximal monotone operator in a Hilbert space and the alternating direction method for the variational inequalities.

本论文主要讨论了求解Hilbert空间上极大单调算子的零点的数值算法以及有限维空间上的变分不等式的交替方向方法。

The existence theorem of solution of approximate problems is obtained.

我们考虑了一类广义似变分不等式系统的数值解，提出和SGVLIP相关的逼近问题，证明了逼近问题解的存在性。

On the basis of the theory of option pricing,We study the connection between America call option and European call option;Under the assumption condition of Black-Scholes formula ,use the theory of martingales and stopping time,get the conclusion that: the price of America call option equals the price of European call option; Discuss some numeric computing methods of the put America option pricing, with the invarional inequaility for optimal stopping, prove the boundary property of America put option price ...

基于期权定价的基本理论，研究美式看涨期权与欧式看涨期权之间的关系；在Black-Sc holes公式假设条件下，利用鞅和停时理论，得美式看涨期权的价格与欧式看涨期权的价格相等；探讨美式看跌期权价格的数字化计算，在相关假设条件下，利用基于最优化时的变分不等式证明了美式看跌期权价格的有界性，并介绍了几种美式看跌期权价格的数字化计算方法。

First, we consider an iterative algorithm of Jacobi type and the corresponding domain decomposition algorithm for a approximate quasivariational inequality system of the Hamilton- Jacobi- Bellman equation and the corresponding convergence problem.

本文研究了逼近Hamilton-Jacobi-Bellman方程的拟变分不等式组的离散问题的Jacobi型迭代算法和Jacobi型区域分解法及其收敛性问题。

The domain decomposition method of Jacobi type for the quasivariational inequality system is proposed and the corresponding monotone convergence theory is established.

然后提出了上述拟变分不等式组的Jacobi型区域分解法，并建立相应的收敛性理论。

Viability Theory is applied to the optimal control problem for switching time varying systems in this dissertation for the first time. The statement about a characterization of the extended value functions as the unique lower semicontinuous solution to a Bensoussan-Lions type QVI is proved.

本文首次将生存理论这一数学工具应用到有限时间切换时变系统的最优控制问题中，得到了最优控制问题的值函数是一类拟变分不等式唯一的下半连续解的重要结论。

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

Hybrid Dynamic; time-varying systems; finite horizon; optimal control; Quasi-Variational Inequality; viscosity solution; lower semicontinuous solution; uniqueness; Dynamic Programming; Viability Theory; inventory systems; mathematical model; proximal subdifferential; parabolic equation; nonlinear boundary

基础科学，数学，控制论、信息论混合动态；时变系统；有限时间；最优控制；拟变分不等式；粘性解；下半连续解；唯一性；动态规划；生存定理；库存系统；数学模型；邻近次微分；抛物型方程；非线性边界

In order to solve the traveler route and departure time choice problem under multiple transportation modes,the variational inequality formulation is proposed in modeling the traveler stochastic dynamic simultaneous route and departure time choice behaviors with elastic demand .

为了解决在多种交通模式条件下出行者的路径与出发时间选择问题，提出了一个变分不等式模型用于模拟具有变需求的多模式随机动态出行选择行为。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。