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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…

Optimization and Control · Mathematics 2018-08-16 Jonathan M. Borwein , Guoyin Li , Matthew K. Tam

We consider sequential iterative processes for the common fixed point problem of families of cutter operators on a Hilbert space. These are operators that have the property that, for any point x\inH, the hyperplane through Tx whose normal…

Functional Analysis · Mathematics 2012-04-20 Andrzej Cegielski , Yair Censor

Given a Hilbert space and a finite family of operators defined on the space, the common fixed point problem (CFPP) is to find a point in the intersection of the fixed point sets of these operators. Instances of the problem have numerous…

Optimization and Control · Mathematics 2025-09-05 Yair Censor , Daniel Reem , Maroun Zaknoon

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each…

Optimization and Control · Mathematics 2020-06-30 Mootta Prangprakhon , Nimit Nimana

We consider the convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. For such an intersection, the convergence rate is known as sublinear in the worst case.…

Optimization and Control · Mathematics 2023-04-27 Hiroyuki Ochiai , Yoshiyuki Sekiguchi , Hayato Waki

In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…

Functional Analysis · Mathematics 2010-10-26 Kristian Bredies , Dirk A. Lorenz

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

Optimization and Control · Mathematics 2021-01-25 Yekini Shehu , Olaniyi. S. Iyiola , Xiao-Huan Li , Qiao-Li Dong

In this paper, we discuss the convergence analysis of the conjugate gradient-based algorithm for the functional linear model in the reproducing kernel Hilbert space framework, utilizing early stopping results in regularization against…

Statistics Theory · Mathematics 2023-10-05 Naveen Gupta , S. Sivananthan , Bharath K. Sriperumbudur

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Optimization and Control · Mathematics 2019-12-05 Xiaokai Chang , Sanyang Liu , Jianchao Bai , Jun Yang

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences…

Optimization and Control · Mathematics 2009-09-21 Jean-Philippe Chancelier

In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…

Functional Analysis · Mathematics 2015-11-11 Vinicius Albani , Peter Elbau , Maarten V. de Hoop , Otmar Scherzer

We provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces. Our results are applied to stochastic instances of common…

Probability · Mathematics 2023-11-01 Neal Hermer , D. Russell Luke , Anja Sturm

This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…

Optimization and Control · Mathematics 2021-08-17 Nicolas Lepage-Saucier

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Optimization and Control · Mathematics 2026-02-17 Patrick L. Combettes , Javier I. Madariaga

Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…

Optimization and Control · Mathematics 2024-04-23 Yonghong Yao , Lateef O. Jolaoso , Yekini Shehu

In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…

Machine Learning · Statistics 2022-11-28 Yuan Mao , Zheng-Chu Guo

In this paper we make a theoretical analysis of the convergence rates of Kaczmarz and Extended Kaczmarz projection algorithms for some of the most practically used control sequences. We first prove an at least linear convergence rate for…

Numerical Analysis · Mathematics 2017-01-30 Constantin Popa

Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…

Machine Learning · Computer Science 2013-05-20 Patrick Hop , Xinghao Pan

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

Functional Analysis · Mathematics 2024-03-18 Guillermina Fongi , María Celeste Gonzalez
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