  The aim of this paper is to develop an efficient algorithm for solving a
class of unconstrained nondifferentiable convex optimization problems in finite
dimensional spaces. To this end we formulate first its Fenchel dual problem and
regularize it in two steps into a differentiable strongly convex one with
Lipschitz continuous gradient. The doubly regularized dual problem is then
solved via a fast gradient method with the aim of accelerating the resulting
convergence scheme. The theoretical results are finally applied to an l1
regularization problem arising in image processing.
