一类边界混合变分不等式的迭代分解方法

Iterative decomposition methods for a kind of boundary mixed variational inequality and its convergence analysis

针对摩擦问题中具不可微泛函项的非线性混合边界变分不等式构造了迭代分解方法 ,讨论了收敛性分析及误差估计 .首先采用正则化方法将原问题变成可微的边界变分不等式 ;其次将问题分解成两个迭代形式的凸泛函极值问题 ,利用标准凸极值问题方法可以求解 ;最后给出了近似解。

Based on the boundary mixed variational inequality with non-differentiable functional in friction problem,the iterative decomposition method and its convergence analysis are presented.First using regularization method,the original problem can be formulated as a differentiable boundary variational inequality.Next we decompose the differentiable problem as two convex optimization sub-problems in the form of iteration,they can be solved by the standard convex optimization method.Finally it presents the convergence analysis and error estimation for the approximation solution and discrete approximation solution.