Related papers: Convergence Rate Analysis for Fixed-Point Iteratio…
Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
We study a fixed point iterative method based on generalized relaxation of strictly quasi-nonexpansive operators. The iterative method is assembled by averaging of strings, and each string is composed of finitely many strictly…
In this paper, we establish sublinear and linear convergence of fixed point iterations generated by averaged operators in a Hilbert space. Our results are achieved under a bounded H\"older regularity assumption which generalizes the…
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving…
Many optimization algorithms$\unicode{x2013}$including gradient descent, proximal methods, and operator splitting techniques$\unicode{x2013}$can be formulated as fixed-point iterations (FPI) of continuous operators. When these operators are…
We in this paper study the nonexpansive operators equipped with arbitrary metric and investigate the connections between firm nonexpansiveness, cocoerciveness and averagedness. The convergence of the associated fixed-point iterations is…
In this work, we develop a convergence framework for iterative algorithms whose updates can be described by a one-parameter family of nonexpansive operators. Within the framework, each step involving one of the main algorithmic operators is…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…
This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlinear solvers in many applications, however a rigorous…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
In this paper, we present a convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration-complexity…
We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local…
Firstly, we invoke the weak convergence (resp. strong convergence) of translated basic methods involving nonexpansive operators to establish the weak convergence (resp. strong convergence) of the associated method with both perturbation and…
Operator splitting techniques have recently gained popularity in convex optimization problems arising in various control fields. Being fixed-point iterations of nonexpansive operators, such methods suffer many well known downsides, which…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…