A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems

Radu Boţ () and Christopher Hendrich ()

Computational Optimization and Applications, 2013, vol. 54, issue 2, 239-262

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. Copyright Springer Science+Business Media New York 2013

Keywords: Fenchel duality; Regularization; Fast gradient method; Image processing (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10589-012-9523-6

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