Proximal minimization in CAT$(κ)$ spaces (1607.03660v2)

Abstract: In this note, we provide convergence results for the proximal point algorithm and a splitting variant thereof in the setting of CAT$(\kappa)$ spaces with $\kappa > 0$ using a recent definition for the resolvent of a convex, lower semi-continuous function due to Kimura and Kohsaka (J. Fixed Point Theory Appl. 18 (2016), 93-115).