变分问题

We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Grding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Grding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Garding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

The problem of solving linear equations changed equivalently into the problem of searching the minimum of unconstrained optimizations of function by variation principle in the paper.

首先通过变分原理将求解线性方程组的问题转化为等价的求解无约束函数最优化问题的极小值。

One of the special case of the problem of finding the zeros is the problem of solving variational inequalities.

变分不等式问题作为极大单调算子的零点问题的特例，其研究的成果更为丰富。

First, we mainly study a class of generalized set-valued vector variational inequality problem.

首先，我们主要研究了一类广义向量集值变分不等式问题，将文献[7]中给出的向量单值情形下的广义L-条件和广义v-强制条件(C_2)推广到向量集值的情形，从而得到新的解的存在性条件，并将它应用到广义向量相补问题_T上。

Variational inequality problem is one of the most important optimization problems, it arises in a widely fields of signal processing, system identification, filter design, robot control, economic science, transprotation science, operational research, and nonlinear analysis fields.

变分不等式问题是一类重要的优化问题，它广泛地出现在信号和图像处理、系统识别、滤波设计、自动控制、经济科学、运输科学、运筹学，非线性分析等领域。

This paper deduces the functional of generalized mixed variational principle for the plane problem of the orthogonal anisotropy, on the basis of which, the generalized mixed finite elements method for the problem is established.

推导了正交各向异性平面问题广义混合变分原理的泛函，以此为基础建立了该问题的有限元广义混合法。

With the similarity between electromagnetical fields and structural mechanics, the electronic E and magnetic H are considered as two duality variables. With the variational principle, the system is introduced into symplectic geometry of Hamiltonian duality equations.

根据电磁场问题与结构力学的类比关系，把电场量E和磁场量H作为二类变量，通过变分原理寻求一般条件下的解法，将体系导入Hamilton对偶方程的辛几何形式，给出了电磁波导的Hamilton辛体系，并给出了辛本征值问题的表达形式。

It is organized as follows:In Chapter 1, we introduce proximal point algorithms" framework and current research situation, optimization problems and variational inequalities" background and current research situation, and some basic concepts and lemmas, which are used in this dissertation.

本文具体安排如下：第一章简要介绍了邻近点算法的基本框架和研究现状，最优化问题和变分不等式问题的背景和研究现状，以及本文需要用到的一些基本概念和引理。

It is known that the VIP can be reformulated as an unconstrained minimization problem through the D-gap function.

我们知道，通过广义D-间隙函数，可以将变分不等式问题转化为一个无约束极小化问题。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。