A hybrid inertial projection-proximal method for variational inequalities

Abdellatif Moudafi (1)

1 GRIMAAG - Groupe de Recherche en Informatique et Mathématiques Appliquées Antilles-Guyane

The hybrid proximal point algorithm introduced by Solodov and Svaiter allowing significant relaxation of the tolerance requirements imposed on the solution of proximal subproblems will be combined with the inertial method introduced by Alvarez and Attouch which incorporates second order information to achieve faster convergence. The weak convergence of the resulting method will be investigated for finding zeroes of a maximal monotone operator in a Hilbert space.

Mots clés: Maximal monotone operators; Weak convergence; Proximal point algorithm; Hybrid projection-proximal method; Resolvent; inertial proximal point scheme

Domaines: Optimisation et contrôle [math.OC]

Abdellatif Moudafi. A hybrid inertial projection-proximal method for variational inequalities. Journal of Inequalities in Pure and Applied Mathematics, 2004, 5 (3), pp.1-5. ⟨hal-00780745⟩