W-convergence of the proximal point algorithm in complete CAT(0) metric spaces
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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 $f: Xrightarrow ]-infty, +infty]$ 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 $f$.
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Journal title
volume 43 issue 3
pages 817- 834
publication date 2017-06-01
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