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In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

Exactly Solvable and Integrable Systems · Physics 2007-11-16 Dan Butnariu , Gabor Kassay

Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…

Optimization and Control · Mathematics 2019-09-06 S. V. Rotin , I. V. Gusakov , V. Ya. Gusakov

We propose in this paper a proximal and contraction method for solving a convex mixed variational inequality problem in a real Hilbert space. To accelerate the convergence of our proposed method, we incorporate an inertial extrapolation…

Optimization and Control · Mathematics 2025-11-25 Chidi Elijah Nwakpa , Austine Efut Ofem , Kalu Okam Okorie , Chinedu Izuchukwu , Chibueze Christian Okeke

In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family…

Functional Analysis · Mathematics 2015-02-18 Vahid Darvish , S. M. Vaezpour

In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…

Functional Analysis · Mathematics 2016-11-01 Zeynab Jouymandi , Fridoun Moradlou

The objective of this research is to explore a convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem. We introduce four inertial extragradient algorithms that are motivated by the…

Optimization and Control · Mathematics 2021-07-27 Bing Tan , Jingjing Fan , Xiaolong Qin

We introduce an abstract algorithm that aims to find the Bregman projection onto a closed convex set. As an application, the asymptotic behaviour of an iterative method for finding a fixed point of a quasi Bregman nonexpansive mapping with…

Functional Analysis · Mathematics 2013-09-26 Heinz H. Bauschke , Jiawei Chen , Xianfu Wang

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

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

Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…

Optimization and Control · Mathematics 2019-08-09 Jose Yunier Bello Cruz , Gemayqzel Bouza Allende

We provide new complexity information for the convergence of the Hybrid Steepest Descent Method for solving the Variational Inequality Problem for a strict contraction on Hilbert space over a closed convex set C given either as the fixed…

Logic · Mathematics 2016-10-04 Daniel Körnlein

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

We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…

Functional Analysis · Mathematics 2022-03-24 Neal Hermer , D. Russell Luke , Anja Sturm

We give a quantitative analysis of a theorem due to Fenghui Wang and Huanhuan Cui concerning the convergence of a multi-parametric version of the proximal point algorithm. Wang and Cui's result ensures the convergence of the algorithm to a…

Functional Analysis · Mathematics 2019-12-24 Bruno Dinis , Pedro Pinto

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 [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…

Dynamical Systems · Mathematics 2010-09-17 A. Zagaris , C. W. Gear , T. J. Kaper , I. G. Kevrekidis

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…

Optimization and Control · Mathematics 2024-09-17 Zheng Zhou , Bing Tan , Songxiao Li

The aim of this paper in to introduce a large class of mappings, called {\it enriched Kannan mappings}, that includes all Kannan mappings and some nonexpansive mappings. We study the set of fixed points and prove a convergence theorem for…

Functional Analysis · Mathematics 2019-09-06 Vasile Berinde , Mădălina Păcurar

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

The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…

Numerical Analysis · Mathematics 2016-02-10 Stefan Kindermann