Convergence rates of a dual gradient method for constrained linear ill-posed problems

Abstract

In this paper we consider a dual gradient method for solving linear ill-posed problems $Ax = y$, where $A : X \to Y$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y$. A strongly convex penalty function is used in the method to select a solution with desired feature. Under variational source conditions on the sought solution, convergence rates are derived when the method is terminated by either an {\it a priori} stopping rule or the discrepancy principle. We also consider an acceleration of the method as well as its various applications.