A Hybrid Steepest-Descent Algorithm for Convex Minimization Over the Fixed Point Set of Multivalued Mappings

Abstract

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications.