2019/06/30 by Bruno Dinis, Juan Dávila, Manuel del Pino +2 · 1 citation
Mathematics · #Algorithm #Applied mathematics #Bounded function #Computer science #Convergence (economics) #Geometric Analysis and Curvature Flows #Interpretation (philosophy) #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems #Operator (biology) #Projection (relational algebra) #Pure mathematics #Set (abstract data type) #Singularity #math.LO #math.OC #msc:03F10 #msc:03F60 #msc:46N10 #msc:47H09 #msc:90C25
paper · pdf · doi:10.1007/s00222-019-00908-y
published as Portugaliae Mathematica 77:3--4 (2020) 345--381 · 21 pages
openalex publication_date 2019/07/27 · openalex created_date 2019/08/13 · arxiv created 2020/03/26 · arxiv updated 2021/01/13 · openalex updated_date 2026/07/23
In this article we use techniques of proof mining to analyse a result, due to Yonghong Yao and Muhammad Aslam Noor, concerning the strong convergence of a generalized proximal point algorithm which involves multiple parameters. Yao and Noor's result ensures the strong convergence of the algorithm to the nearest projection point onto the set of zeros of the operator. Our quantitative analysis, guided by Fernando Ferreira and Paulo Oliva's bounded functional interpretation, provides a primitive recursive bound on the metastability for the convergence of the algorithm, in the sense of Terence Tao. Furthermore, we obtain quantitative information on the asymptotic regularity of the iteration. The results of this paper are made possible by an arithmetization of the \limsup.