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.
Maximal monotone operator proximal point algorithm Hadamard space nonexpansive mapping resolvent operator
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Publication Date | February 6, 2020 |
Published in Issue | Year 2020 Volume: 49 Issue: 1 |