In this thesis, we consider the finite monotone variational inequality problem V I P in a systematic way. V I P consists in finding a solution ;In short, the contributions of the thesis are: (1) A literature review of the V I P theory and algorithms is given; (2) A general descent framework for the V I P equivalent optimization problem is established with a detailed analysis; (3) An inexact method is developed for the V I P; (4) a global convergence proof is given for the linearized Jacobi method for V I P
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机译：在本文中，我们系统地考虑了有限单调变分不等式问题。 V I P在于寻找解决方案；总而言之，本文的贡献是：（1）给出了关于V I P理论和算法的文献综述； （2）通过详细分析，建立了针对V I P等价优化问题的通用下降框架； （3）为V I P开发了一种不精确的方法； （4）给出了V I P的线性Jacobi方法的全局收敛性证明
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