A viscosity proximal point algorithm for solving optimization problems in Hadamard spaces

Abstract

The main purpose of this paper is to introduce a modified viscosity-type proximal point algorithm and prove its strong convergence to a zero of a monotone operator, which is also a minimizer of a proper convex and lower semi-continuous function and a fixed point of a demicontractive-type (or demimetric) mapping in an Hadamard space. We apply the results obtained to solve variational inequality problems in Hadamard spaces. To further show the applicability and the advantages of the obtained results, several numerical experiments of our algorithm in comparison with that studied by Ranjbar and Khatibzadeh [Mediterranean Journal of Mathematics 14(2017), 15 pp.] are carried out in the framework of Hadamard spaces. Our results improve and generalize some recent important results in the literature.