Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function

Jean-Philippe Chancelier (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principle or inexact variable metric forward-backward algorithm. Assuming that the global objective function satisfies the Kurdyka-Lojasiewicz inequality we prove the convergence of the proposed algorithm weakening assumptions found in previous works.

Mots clés: Nonconvex nonsmooth optimization; Forward-Backward splitting; Auxiliary problem principle; Kurdyka-Lojasiewicz inequality

Domaines: Optimisation et contrôle [math.OC]

Jean-Philippe Chancelier. Auxiliary problem principle and inexact variable metric forward-backward algorithm for minimizing the sum of a differentiable function and a convex function. 2015. ⟨hal-01183854⟩