Related papers: An application of proof mining to the proximal poi…

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…

We prove an abstract form of the strong convergence of the Halpern-type and Tikhonov-type proximal point algorithms in CAT(0) spaces. In addition, we derive uniform and computable rates of metastability (in the sense of Tao) for these…

This paper provides an effective uniform rate of metastability (in the sense of Tao) on the strong convergence of Halpern iterations of nonexpansive mappings in CAT(0) spaces. The extraction of this rate from an ineffective proof due to…

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…

We use techniques of proof mining to extract a uniform rate of metastability (in the sense of Tao) for the strong convergence of approximants to fixed points of uniformly continuous pseudocontractive mappings in Banach spaces which are…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

We provide quantitative information in the form of a rate of metastability in the sense of T. Tao and (under a metric regularity assumption) a rate of convergence for an algorithm approximating zeros of differences of maximally monotone…

In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly convex Banach…

We use techniques originating from the subdiscipline of mathematical logic called `proof mining' to provide rates of metastability and - under a metric regularity assumption - rates of convergence for a subgradient-type algorithm solving…

We use techniques of proof mining to extract computable and uniform rates of metastability (in the sense of Tao) for iterations of continuous functions on the unit interval, firstly (following earlier work of Gaspar) out of convergence…

Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of probabilistic statements. As a main result, this translation…

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,…

We compute uniform rates of metastability for the Ishikawa iteration of a Lipschitz pseudo-contractive self-mapping of a compact convex subset of a Hilbert space. This extraction is an instance of the proof mining program that aims to apply…

Using proof-theoretical techniques, we analyze a proof by H.-K. Xu regarding a result of strong convergence for the Halpern type proximal point algorithm. We obtain a rate of metastability (in the sense of T. Tao) and also a rate of…

This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs.…

We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear (separable) Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field and prove its convergence…

We apply proof mining methods to analyse a result of Boikanyo and Moro\c{s}anu on the strong convergence of a Halpern-type proximal point algorithm. As a consequence, we obtain quantitative versions of this result, providing uniform…

This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract…

In this paper, we obtain rates of metastability for the Tikhonov-Mann iteration for countable families of mappings in CAT(0) spaces. This iteration was recently defined by the author in the setting of W-hyperbolic spaces as a generalization…

A generalized method of alternating resolvents was introduced by Boikanyo and Moro{\c s}anu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two…