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

Abstract

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