Extended Forward-Backward Algorithm

Marc Lassonde (1) , Ludovic Nagesseur (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence generated by the algorithm under assumptions similar to those used in classical forward-backward algorithms. This provides as a special case an algorithm for solving convex constrained minimization problems without qualification condition.

Domaines: Optimisation et contrôle [math.OC]

Marc Lassonde, Ludovic Nagesseur. Extended Forward-Backward Algorithm. Journal of Mathematical Analysis and Applications, 2013, 403 (1), pp.167-172. ⟨10.1016/j.jmaa.2013.02.022⟩. ⟨hal-00761657⟩