A double smoothing technique for solving unconstrained nondifferentiable convex optimization problems
- 414 Downloads
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.
KeywordsFenchel duality Regularization Fast gradient method Image processing
- 3.Beck, A., Teboulle, M.: Gradient-based algorithms with applications to signal recovery problems. In: Eldar, Y., Palomar, D. (eds.) Convex Optimization in Signal Processing and Communications, pp. 33–88. Cambridge University Press, Cambridge (2010) Google Scholar