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.

Keywords:

• Splitting method
• proximal point algorithm
• minimization
• convex function
• ergodic convergence
• Hadamard space

Mathematics Subject Classifications (2020):

• Primary: 90C25
• 90C48
• Secondary:65K10

Acknowledgments

The authors are grateful to the referee(s) for valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).