W-convergence of the proximal point algorithm in complete CAT(0) metric spaces

In this paper, we generalize the proximal point algorithm to complete CAT(0) spaces and show that the sequence generated by the proximal point algorithm w-converges to a zero of the maximal mono tone operator. Also, we prove that if f : X→] -∞;+∞] is a proper, convex and lower semicontinuous function on the complete CAT(0) space X, then the proximal point algorithm w-converges to a zero of the sub- differential of f, i.e., a minimizer of f. Some strong convergence results (convergence in metric) are also presented with additional assumptions on the monotone operator and the convex function f.