Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces

Hedy Attouch (1) , Patrick Redont (1) , Benar Fux Svaiter (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMPA

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of Levenberg-Marquardt type and acts in an open-loop or closed-loop form. In the open-loop case the regularization termmay be of bounded variation.

Mots clés: Newton-type methods; Monotone inclusions; Convex optimization; Closed-loop regularization; BV controls; Levenberg-Marquardt method

Domaines: Optimisation et contrôle [math.OC]

Hedy Attouch, Patrick Redont, Benar Fux Svaiter. Global convergence of a closed-loop regularized Newton method for solving monotone inclusions in Hilbert spaces. Journal of Optimization Theory and Applications, 2012, Published online (Published online), pp.Published online 21 November 2012. ⟨10.1007/s10957-012-0222-3⟩. ⟨hal-00803194⟩