A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems

Authors:
Radu Ioan Boţ;Christopher Hendrich
Affiliations:
Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany 09107;Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany 09107
Venue:
Computational Optimization and Applications
Year:
2013

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Abstract

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 l 1 regularization problem arising in image processing.