  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.
