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.
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R.I. Boţ’s research is partially supported by DFG (German Research Foundation), project BO 2516/4-1.
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Boţ, R.I., Hendrich, C. A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems. Comput Optim Appl 54, 239–262 (2013). https://doi.org/10.1007/s10589-012-9523-6
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DOI: https://doi.org/10.1007/s10589-012-9523-6