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A line-search based proximal algorithm for convex and non-convex optimization, with applications to image processing

par Loris, Ignace
Référence Optimization Techniques for Inverse Problems III Workshop (19-21/09/2016: Modena, Italy)
Publication Non publié, 2016-09-20

Communication à un colloque

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Résumé :

A novel iterative algorithm for the solution of convex or non-convex optimization problems is presented. In particular, the objective function is assumed to be the sum of a differentiable (possibly non-convex) part and a convex (possibly non-differentiable) part. The proposed algorithm is based on an Armijo line-search rule and uses the gradient of the smooth part and the proximal operator of the non-smooth part. However, the proximal operator does not have to be computed exactly and verifiable criteria for its inexact computation are given in some cases of practical interest.In general we prove that all limit points of the iterates are stationary, while in the special case of a convex objective function we prove the convergence of the whole sequence to a minimizer. In the non-convex case, we also show convergence if the objective function satisfies the Kurdyka- Lojasiewicz property at each point of its domain. Finally, the algorithm is applied to a wide range of image reconstruction problems. This presentation is based on joint work with S. Bonettini, F. Porta, M. Prato and S. Rebegoldi.