Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces
Bruno Dinis, Pedro Pinto
Abstract
In this paper we consider, in the general context of CAT(0) spaces, an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations. We prove, under suitable conditions, the strong convergence of this algorithm, benefi ting from ideas from the proof mining program. We give quantitative information in the form of effective rates of asymptotic regularity and of metastability (in the sense of Tao). Motivated by these results we are also able to obtain strongly convergent versions of the forward-backward and the Douglas-Rachford algorithms. Our results generalize recent work by Bot, Csetnek and Meier, and Cheval and Leustean.
Topics & Concepts
MathematicsSchema (genetic algorithms)Convergence (economics)Context (archaeology)Applied mathematicsComputer scienceEconomicsPaleontologyMachine learningBiologyEconomic growthOptimization and Variational AnalysisAdvanced Banach Space TheoryApproximation Theory and Sequence Spaces