- Hacettepe Journal of Mathematics and Statistics
- Vol: 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 Tahernia, Sirous Moradi, Somayeh Jafari
Pages : 399-408
Doi:10.15672/hujms.470975
View : 8 | Download : 2
Publication Date : 2020-02-06
Article Type : Research
Abstract :In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CAT(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