An Implicit Extragradient Method for Hierarchical Variational Inequalities [PDF]
Fixed Point Theory and Applications, 2011 As a well-known numerical method, the extragradient method solves numerically the variational inequality of finding such that , for all . In this paper, we devote to solve the following hierarchical variational inequality Find such that , for
Liou YeongCheng, Yao Yonghong
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Parallel Extragradient-Proximal Methods for Split Equilibrium Problems [PDF]
Mathematical Modelling and Analysis, 2016 In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method.
Dang Van Hieu
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Extended Extragradient Methods for Generalized Variational Inequalities [PDF]
Journal of Applied Mathematics, 2012 We suggest a modified extragradient method for solving the generalized variational inequalities in a Banach space. We prove some strong convergence results under some mild conditions on parameters. Some special cases are also discussed.
Yonghong Yao +3 more
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A Mean Extragradient Method for Solving Variational Inequalities [PDF]
Symmetry, 2021 We propose a modified extragradient method for solving the variational inequality problem in a Hilbert space. The method is a combination of the well-known subgradient extragradient with the Mann’s mean value method in which the updated iterate is picked in the convex hull of all previous iterates.
Apichit Buakird +2 more
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Extragradient methods for solving nonconvex variational inequalities [PDF]
Journal of Computational and Applied Mathematics, 2011 This paper is devoted to the study of a new class of variational inequalities (the nonconvex variational inequalities), and for a new class of nonconvex sets (uniformly prox-regular set \(K_r\)). This class of uniformly prox-regular sets have played an important part in many nonconvex applications (optimization, dynamic systems and differential ...
Muhammad Aslam Noor +3 more
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Modified Noor's Extragradient Method for Solving Generalized Variational Inequalities in Banach Spaces [PDF]
Abstract and Applied Analysis, 2012 Motivated and inspired by Korpelevich's and Noor's extragradient methods, we suggest an extragradient method by using the sunny nonexpansive retraction which has strong convergence for solving the generalized variational inequalities in Banach spaces.
Shunhou Fan +3 more
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G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph [PDF]
Examples and CounterexamplesIn this article, we introduce the G-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving G-variational inequality problems in Hilbert space.
Monika Swami, M.R. Jadeja
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An Accelerated Extragradient Method for Solving Pseudomonotone Equilibrium Problems with Applications [PDF]
Axioms, 2020 Several methods have been put forward to solve equilibrium problems, in which the two-step extragradient method is very useful and significant. In this article, we propose a new extragradient-like method to evaluate the numerical solution of the ...
Nopparat Wairojjana +3 more
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On a General Extragradient Implicit Method and Its Applications to Optimization [PDF]
Symmetry, 2020 Let X be a Banach space with both q-uniformly smooth and uniformly convex structures. This article introduces and considers a general extragradient implicit method for solving a general system of variational inequalities (GSVI) with the constraints of a common fixed point problem (CFPP) of a countable family of nonlinear mappings { S n } n = 0
Lu-Chuan Ceng, Qing Yuan
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Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces [PDF]
Abstract and Applied Analysis, 2012 The purpose of this paper is to introduce a new modified relaxed extragradient method and study for finding some common solutions for a general system of variational inequalities with inversestrongly monotone mappings and nonexpansive mappings in the ...
Yuanheng Wang, Liu Yang
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