Two proximal splitting methods in Hadamard spaces

Abstract

Motivated by computing medians and means, two proximal splitting methods, backward-backward scheme introduced by Passty [Ergodic convergence to a zero of the sum of monotone operators in Hilbert spaces. J Math Anal Appl. 1979;72:383–390.] and barycentric method introduced by Lehdili and Lemaire [Metric spaces of non-positive curvature. Berlin: Springer; 1999.] are investigated in Hadamard space setting. A weak ergodic convergence theorem and some strong convergene results for both schemes are studied.