On the acceleration of the double smoothing technique for unconstrained convex optimization problems
| Autor: | Christopher Hendrich, Radu Ioan Boţ |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Convex analysis
Mathematical optimization Control and Optimization Optimization problem Applied Mathematics Duality (optimization) Perturbation function 90C25 90C46 47A52 Management Science and Operations Research Optimization and Control (math.OC) Convex optimization Proximal gradient methods for learning FOS: Mathematics Convex function Gradient method Mathematics - Optimization and Control Mathematics |
| Popis: | In this article we investigate the possibilities of accelerating the double smoothing technique when solving unconstrained nondifferentiable convex optimization problems. This approach relies on the regularization in two steps of the Fenchel dual problem associated to the problem to be solved into an optimization problem having a differentiable strongly convex objective function with Lipschitz continuous gradient. The doubly regularized dual problem is then solved via a fast gradient method. The aim of this paper is to show how do the properties of the functions in the objective of the primal problem influence the implementation of the double smoothing approach and its rate of convergence. The theoretical results are applied to linear inverse problems by making use of different regularization functionals. 22 pages. arXiv admin note: text overlap with arXiv:1203.2070 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|