变分不等式

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

Generalized strong vector variational-like inequalities; Minty's lemma; KKM mapping; pseudomonotone; Ky Fan lemma; open mapping theorem; complete; the second category; conjugate; proper convex lower semicontinuous function; linear mapping; closedness

基础科学，数学，数学分析广义强向量似变分不等式； Minty引理； KKM映象；伪单调； Ky Fan引理；开映射定理；完备；第二纲；共轭；真凸下半连续函数；线性映射；闭性

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

HJB equation; quasivariational inequality; domain decomposition; convergence; iterative algorithm; relaxation algorithm; existence; multigrid method

基础科学，数学，数学分析HJB方程；拟变分不等式；区域分解；收敛性；迭代法；松弛算法；存在性；多重网格法

In this paper,we consider necessary conditions for optional control of second order ordinary differential equation with coefficient control and two point boundary value,thenobtain the inequality of variation.

在这篇文章中，我们考虑控制出现在最高阶系数上二阶常微分方程系统最优控制满足的必要条件，得到了最优控制满足的变分不等式。

Keywords: meshless method;adaptive algorithm;elliptic equation; variational inequality.

中文关键词：无网格方法；自适应算法；椭圆型方程；变分不等式

The solution of the linear variational inequality problem is transmuted to an equilibrium point of neural networks.

线性变分不等式问题的解被转化为神经网络的平衡点。

Furthermore, by exploiting existence theorem, algorithms for SNVI are constructed and the convergence of the algorithm is discussed.

最后，我们讨论了Banach空间中混合非线性变分不等式系统的数值算法。

In the paper, Existence theorem for generalized variational inequalities is established in locally FC-spaces space and its applications are presented.

文章提供关于局部FC-空间上的广义变分不等式的存在性定理，并给出它的一些应用。

Finally, the perturbation problems for the mixed variational-like inequalities problems are discussed, and the existence and uniqueness theorem of the solutions for the perturbation problems is also proved.

最后，讨论了混合似变分不等式问题的扰动问题，并证明了扰动问题的解的存在唯一性定理。

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。