The modified proximal point algorithm in Hadamard spaces

Abstract

Abstract The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.

Keywords

• Hadamard space
• CAT ( 0 ) $\operatorname{CAT}(0)$ space
• Moreau–Yosida resolvent
• Implicit iterative rule
• Proximal point algorithm
• Variational inequality