@article {
author = {Ranjbar, S.},
title = {W-convergence of the proximal point algorithm in complete CAT(0) metric spaces},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {3},
pages = {817-834},
year = {2017},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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 monotone operator. Also, we prove that if $f: X\rightarrow ]-\infty, +\infty]$ 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 subdifferential 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 $f$.},
keywords = {Keywords: Hadamard space,maximal monotone operator,Proximal point algorithm,w-convergence,Subdifferential},
url = {http://bims.iranjournals.ir/article_971.html},
eprint = {http://bims.iranjournals.ir/article_971_82f5acff6dbe281bad8d1a4e7301a6f6.pdf}
}