- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 3 Issue: 4
- The proximal point algorithm in complete geodesic spaces with negative curvature
The proximal point algorithm in complete geodesic spaces with negative curvature
Authors : Takuto Kajimura, Yasunori KİMURA
Pages : 192-200
Doi:10.31197/atnaa.573972
View : 4 | Download : 3
Publication Date : 2019-12-30
Article Type : Research
Abstract :The proximal point algorithm is an approximation method for finding a minimizer of a convex function. In this paper, we introduce the resolvent for a convex function in complete geodesic spaces with negative curvature. Using properties of the resolvent, we show the proximal point algorithm in complete geodesic spaces with negative curvature.Keywords : CAT($-1$) space, proximal point algorithm, resolvent, convex function