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

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:1
The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces

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

Authors : Mohsen TAHERNİA, Sirous MORADİ, Somayeh JAFARİ

Pages : 399-408

Doi:10.15672/hujms.470975

View : 53 | Download : 12

Publication Date : 2020-02-06

Article Type : Research Paper

Abstract :In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CATinsert ignore into journalissuearticles values(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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