研究了一类非线性变分不等式系统(SNVI)及其相关辅助问题，建立了辅助问题解的存在性定理。
We consider a kind of system of nonlinear variational inequalities (SNVI) and its related auxiliary problems.
延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式。
The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values.
其次，利用该存在性结果，给出了解这类广义强非线性混合似变分不等式的迭代算法。
Secondly, the iterative algorithm for solving this class of generalized strongly nonlinear mixed variational-like inequalities is given by using this existence result.
本文延拓辅助原理的技巧，来研究一类广义集值强非线性混合似变分不等式。
The auxiliary principle technique is extended to investigate a class of generalized set-valued strongly nonlinear variational-like inequalities.
它与不动点理论，变分不等式问题，线性和非线性分析，以及其他领域的应用数学如经济，平衡问题等都有密切的联系。
It has an important relation with stationary point theories, variational inequality, linear and nonlinear analysis, and some applied mathematical problems such as economic and equilibrium problems.
本文主要讨论求解非线性方程组问题与变分不等式问题的迭代算法。全文共分三章。
This thesis includes three chapters, which mainly discusses the iterative algorithms for solving nonlinear equations problems and nonlinear variational inequality problems.
首先，证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性。
Firstly, the existence of solutions to the auxiliary problems for this class of generalized strongly nonlinear mixed variational-like inequalities is shown.
在每步迭代计算中，新方法提出了易于计算的子问题，该子问题由强单调的线性变分不等式和良态的非线性方程系统构成。
At each iteration, the proposed subproblem consists of a strongly monotonic linear variational inequality and a well-conditioned system of nonlinear equations, which is easily to be solved.
第三部分，利用辅助原理研究了广义集值非线性混合似变分不等式的解的存在性，收敛性及算法的稳定性。
In the last section, we introduce and study a class of variational-like inequalities by applying the auxiliary principle technique.
引进一类广义非线性向量似变分不等式，建立其解存在的充分条件。
Last, a kind of generalized nonlinear vector variational-like inequalities is presented and the solution existence for this kind of variational inequalities is given.
然后，利用辅助原理技巧，构造了求解广义非线性混合拟似变分不等式问题的迭代算法。
So, in chapter 3, we consider how to use predictor-corrector algorithm to solve some variational inequalities.
然后，利用辅助原理技巧，构造了求解广义非线性混合拟似变分不等式问题的迭代算法。
So, in chapter 3, we consider how to use predictor-corrector algorithm to solve some variational inequalities.
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