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In this paper, we consider a new iteration process which is faster than all of Picard, Mann, Ishikawa and Agarwal et al. processes. We also prove some strong and weak convergence theorems for the class of nonexpansive mappings in Banach…

Functional Analysis · Mathematics 2016-02-09 Nazli Kadioglu , Isa Yildirim

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

Optimization and Control · Mathematics 2023-12-05 Yurii Nesterov

In this paper, we consider the Halpern iteration scheme for a finite family of quasinonexpansive mappings and then prove a strong convergence theorem to their common fixed point in a complete geodesic space with curvature bounded above by…

Functional Analysis · Mathematics 2019-11-19 Tatsuki Ezawa , Yasunori Kimura

In this article we investigate a finite element formulation of strongly monotone quasi-linear elliptic PDEs in the context of fixed-point iterations. As opposed to Newton's method, which requires information from the previous iteration in…

Numerical Analysis · Mathematics 2015-07-01 Scott Congreve , Thomas P. Wihler

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.…

Optimization and Control · Mathematics 2018-04-19 Laurentiu Leustean , Adriana Nicolae , Andrei Sipos

In this paper, using sunny generalized nonexpansive retraction, we propose new extragradient and linesearch algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a…

Functional Analysis · Mathematics 2016-06-07 Zeynab Jouymandi , Fridoun Moradlou

This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…

Optimization and Control · Mathematics 2015-10-22 Hideaki Iiduka

We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Chinedu Izuchukwu , Chibueze CHristian Okeke , Dilber Uzun Ozsahin , Abubakar Adamu

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

Optimization and Control · Mathematics 2017-11-29 Regina S. Burachik , R. Díaz Millán

We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…

Numerical Analysis · Mathematics 2016-01-07 Robert M. Gower , Peter Richtárik

In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of…

Probability · Mathematics 2017-01-24 Bahia Barache , Idir Arab , Abdelnasser Dahmani

We introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

Optimization and Control · Mathematics 2015-12-31 J. Y. Bello Cruz , R. Diaz Millan

Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…

Optimization and Control · Mathematics 2022-12-26 Xiao Li , Zhihui Zhu , Anthony Man-Cho So , Jason D Lee

We use proof mining techniques to obtain a uniform rate of asymptotic regularity for the instance of the parallel algorithm used by L\'opez-Acedo and Xu to find common fixed points of finite families of $k$-strict pseudocontractive…

Functional Analysis · Mathematics 2016-06-21 Andrei Sipos

We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…

Quantum Physics · Physics 2025-12-23 Shrigyan Brahmachari , Roberto Rubboli , Marco Tomamichel

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky

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

In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in a Banach space. Our results…

Functional Analysis · Mathematics 2014-10-16 Sattar Alizadeh , Fridoun Moradlou

The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the…

Optimization and Control · Mathematics 2014-08-15 Heinz H. Bauschke , Caifang Wang , Xianfu Wang , Jia Xu