Convergence Rate Analysis for Splitting Methods

Operator splitting methods play a fundamental theoretical and algorithmic role in various areas of scientific computing, and have inspired many efficient numerical algorithms in different applications. The numerical efficiency and some theoretical progress on this type of method have long been witnessed in diversified areas, but research on their convergence rates is in its infancy. In this project we will focus on the context of convex optimization, and intensively investigate the convergence rates of some fundamental operator splitting methods. For these methods, we will estimate their worst-case convergence rates in generic settings, and sharper convergence rates in specific settings