Convergence rates results for Tikhonov regularization of nonlinear ill-posed operator equations in abstract function spaces require the handling of both smoothness conditions imposed on the solution and structural conditions expressing the character of nonlinearity. Recently, the distinguished role of variational inequalities holding on some level sets was outlined for obtaining convergence rates results. When lower rates are expected such inequalities combine the smoothness properties of solution and forward operator in a sophisticated manner. In this paper, using a Banach space setting we are going to extend the variational inequality approach from Hölder rates to more general rates including the case of logarithmic convergence rates.
Deep Domain Decomposition Method for Solving the Variational Inequality Problems
School of Mathematics and Computing Science, Guilin University of Electronics Technology（桂林电子科技大学数学与计算科学学院）；Center for Applied Mathematics of Guangxi (GUET)（广西应用数学中心）
A generalized strong convergence algorithm in the presence of the errors for the variational inequality problems in Hilbert spaces
本文研究了求解变分不等式问题的一种算法的强收敛性，该算法推广了Thong et al，Numerical Algorithms. 78，1045-1060（2018））。我们已经减少和改进了他们的算法的一些条件，我们已经证明了算法的收敛性存在一些计算误差。然后利用MATLAB软件，通过数值算例对结果进行了说明.最后，我们比较了我们的算法与其他一些著名的算法。
