The proximal point algorithm in complete geodesic spaces with negative curvature

Year 2019, Volume: 3 Issue: 4, 192 - 200, 30.12.2019

Takuto Kajimura , Yasunori Kimura

https://doi.org/10.31197/atnaa.573972

Cited By: 1

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

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