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Computational Optimization and Applications

, Volume 54, Issue 2, pp 239–262 | Cite as

A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems

  • Radu Ioan Boţ
  • Christopher Hendrich
Article

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.

Keywords

Fenchel duality Regularization Fast gradient method Image processing 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany

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