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

Abstract

AbstractIn this paper we consider a dual gradient method for solving linear ill-posed problems $$Ax = y$$ A x = y , where $$A : X \rightarrow Y$$ A : X → 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 a priori stopping rule or the discrepancy principle. We also consider an acceleration of the method as well as its various applications.