The proximal point algorithm in complete geodesic spaces with negative curvature

Open Access

Original research article

Author(s):

Takuto Kajimura, Yasunori Kimura

Department of Information Science, Toho University, Funabashi, Chiba 274-8510, Japan

Advances in the Theory of Nonlinear Analysis and its Applications 3(4), 192-200.

Received: June 7, 2019

Accepted: October 6, 2019

Published: October 9, 2019

Abstract

The proximal point algorithm is an approximation method used to find a minimizer of a convex function. In this work, leveraging the properties of the resolvent proposed by the authors, we establish the proximal point algorithm using a suitable notion of weak convergence in complete geodesic spaces with negative curvature.

Keywords: CAT(−1) space, proximal point algorithm, resolvent, convex function, geodesic space.

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APA Style

Kajimura, T., & Kimura, Y. (2019). The proximal point algorithm in complete geodesic spaces with negative curvature. Advances in the Theory of Nonlinear Analysis and its Application, 3(4), 192-200.