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The aim of this paper is to develop an efficient algorithm for solving aclass of unconstrained nondifferentiable convex optimization problems in finitedimensional spaces. To this end we formulate first its Fenchel dual problem andregularize it in two steps into a differentiable strongly convex one withLipschitz continuous gradient. The doubly regularized dual problem is thensolved via a fast gradient method with the aim of accelerating the resultingconvergence scheme. The theoretical results are finally applied to an l1regularization problem arising in image processing.

A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems