Effective strong convergence of the proximal point algorithm in CAT(0) spaces

2018/01/07 by Leustean, Laurentiu, Sipos, Andrei · 1 citation
#03F10 #46N10 #47J25 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1801.02179

Abstract

We apply methods of proof mining to obtain uniform quantitative bounds on the strong convergence of the proximal point algorithm for finding minimizers of convex, lower semicontinuous proper functions in CAT(0) spaces. Thus, for uniformly convex functions we compute rates of convergence, while, for totally bounded CAT(0) spaces we apply methods introduced by Kohlenbach, the first author and Nicolae to compute rates of metastability.

Cited by

• Mean-square and linear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature

Related

• An abstract proximal point algorithm
• An application of proof mining to the proximal point algorithm in CAT(0) spaces
• Proximal minimization in CAT(κ) spaces
• Quantitative results on a Halpern-type proximal point algorithm
• A rate of metastability for the Halpern type Proximal Point Algorithm