Métodos de proyección tipo promedio de cuerdas en espacios de Hadamard

Abstract

Given an Hadamard space (H,d) and C1,…,Cm ⊆ H nonempty, closed and convex subsets of H, such that their intersection C:= C1⋂…⋂ Cm, is nonempty, the Convex Feasibility Problem aims to find an element in C. In this project, we adapt a string-averaging projection method, which involves the projection operators over the sets C1,…,Cm, in order to solve the Convex Feasibility Problem in Hadamard Spaces. We also study the convergence of this method. Originally, this string-averaging projection method was developed for Hilbert spaces. Furthermore, we extend this result when, instead of the projection operators, we use possibly discontinuous approximations of such operators, in the framework of homogeneous Hadamard spaces.