Convergence Analysis of Proximal Point Algorithm in Geodesic Spaces

Abstract

In this work, we aim to devise an implicit proximal algorithm to find an approximate common solution associated with the convex optimization problem and the fixed point problem of non-expansive mappings in Hadamard spaces. The convergence analysis of the proposed algorithm guarantees the strong convergence characteristics as well as convergence characteristics under suitable set of control conditions. Moreover, we extended our results from the case of single mapping to the case of family of mappings.