Proximal minimization in CAT(κ) spaces

2016/07/13 by Rafa Espínola, Espínola, Rafa, Adriana Nicolae +1
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Advanced Banach Space Theory #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.1607.03660

Abstract

In this note, we provide convergence results for the proximal point algorithm and a splitting variant thereof in the setting of CAT(κ) spaces with κ> 0 using a recent definition for the resolvent of a convex, lower semi-continuous function due to Kimura and Kohsaka (J. Fixed Point Theory Appl. 18 (2016), 93-115).

Citations

• The proximal point algorithm in metric spaces

Related

• Effective strong convergence of the proximal point algorithm in CAT(0) spaces
• An abstract proximal point algorithm
• Proximal Point Algorithm for Quasi-convex Minimization Problems in metric spaces
• The proximal point algorithm in metric spaces
• Local convergence of an inexact proximal algorithm for weakly convex functions