Stochastic Regularization Method for Linear Ill-posed Problems

Due to rapid growth of data sizes in practical applications, in recent years stochastic optimization methods have received tremendous attention and proved to be efficient in various applications of science and technology including in particular the machine learning applications. In this talk we propose randomized Kaczmarz method, stochastic gradient descent method and stochastic mirror descent method for solving linear ill-posed inverse problems. The convergence and convergence rate are provided. Several numerical examples validate the efficiency of the proposed algorithms.