The asymptotic behavior of a class of nonlinear semigroups in Hadamard\n spaces

2014/05/26 by Miroslav Bačák, Simeon Reich, Bacak, Miroslav +1
Computer Science · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Primary: 47H20 #secondary: 60J45

paper · pdf · doi:10.48550/arxiv.1405.6637

openalex publication_date 2014/05/26 · openalex created_date 2022/08/20 · openalex updated_date 2026/07/28

Abstract

We study a nonlinear semigroup associated to a nonexpansive mapping on a\nHadamard space and establish its weak convergence to a fixed point. A\ndiscrete-time counterpart of such a semigroup, the proximal point algorithm,\nturns out to have the same asymptotic behavior. This complements several\nresults in the literature -- both classical and more recent ones. As an\napplication, we obtain a new approach to heat flows in singular spaces for\ndiscrete, as well as continuous times.\n

Citations

• The proximal point algorithm in metric spaces

Related

• Convergence of nonlinear semigroups under nonpositive curvature
• Spatial asymptotics and equilibria of heat flow on ℝ^d
• Measurable Semigroup Selection of the Heat Flow for Harmonic Maps
• On the proximal point algorithm for strongly quasiconvex functions in Hadamard spaces
• Metric projection and convergence theorems for nonexpansive mappings in Hadamard spaces