The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces

Year 2020, Volume: 49 Issue: 1, 399 - 408, 06.02.2020

Mohsen Tahernia Sirous Moradi , Somayeh Jafari

https://doi.org/10.15672/hujms.470975

Abstract

In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CAT(0) spaces. First, a necessary and sufficient condition is presented for the zero set of the operator to be nonempty. Afterwards, we prove that, under suitable conditions, the proposed algorithm converges strongly to the metric projection of some point onto the zero set of the involving maximal monotone operator.

Keywords

Maximal monotone operator, proximal point algorithm, Hadamard space, nonexpansive mapping, resolvent operator

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