Asymptotic convergence of an inertial proximal method for unconstrained quasiconvex minimization

Authors:
Paul-Emile Maingé
Affiliations:
Département Scientifique Interfacultaire, GRIMAAG, Université des Antilles et de la Guyane, Cedex, Martinique (F.W.I.), France 97230
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

This paper deals with the convergence analysis of a second order proximal method for approaching critical points of a smooth and quasiconvex objective function defined on a real Hilbert space. The considered method, well-known in the convex case, unifies proximal method, relaxation and inertial-type extrapolation. The convergence theorems established in this new setting improve recent ones.