Alternated inertial subgradient extragradient method for equilibrium problems

Top ◽  
2021 ◽  
Author(s):  
Yekini Shehu ◽  
Qiao-Li Dong ◽  
Lulu Liu ◽  
Jen-Chih Yao
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method

scholarly journals Approximation Results for Equilibrium Problems Involving Strongly Pseudomonotone Bifunction in Real Hilbert Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 137
Author(s):  
Wiyada Kumam ◽  
Kanikar Muangchoo
Keyword(s):  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Extragradient Method ◽  
Minimax Problems ◽  
Strong Convergence Theorem ◽  
Test Problems ◽  
Subgradient Extragradient Method ◽  
Step Size ◽  
Pseudomonotone Bifunction ◽  
Equilibrium Test

A plethora of applications in non-linear analysis, including minimax problems, mathematical programming, the fixed-point problems, saddle-point problems, penalization and complementary problems, may be framed as a problem of equilibrium. Most of the methods used to solve equilibrium problems involve iterative methods, which is why the aim of this article is to establish a new iterative method by incorporating an inertial term with a subgradient extragradient method to solve the problem of equilibrium, which includes a bifunction that is strongly pseudomonotone and meets the Lipschitz-type condition in a real Hilbert space. Under certain mild conditions, a strong convergence theorem is proved, and a required sequence is generated without the information of the Lipschitz-type cost bifunction constants. Thus, the method operates with the help of a slow-converging step size sequence. In numerical analysis, we consider various equilibrium test problems to validate our proposed results.

scholarly journals Inertial Optimization Based Two-Step Methods for Solving Equilibrium Problems with Applications in Variational Inequality Problems and Growth Control Equilibrium Models

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3292 ◽  
Author(s):  
Habib ur Rehman ◽  
Poom Kumam ◽  
Meshal Shutaywi ◽  
Nasser Aedh Alreshidi ◽  
Wiyada Kumam
Keyword(s):  
Variational Inequality ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Mathematical Finance ◽  
Convergence Result ◽  
Variational Inequality Problems ◽  
Subgradient Extragradient Method ◽  
Pseudomonotone Operator ◽  
Equilibrium Models ◽  
Variable Stepsize

This manuscript aims to incorporate an inertial scheme with Popov’s subgradient extragradient method to solve equilibrium problems that involve two different classes of bifunction. The novelty of our paper is that methods can also be used to solve problems in many fields, such as economics, mathematical finance, image reconstruction, transport, elasticity, networking, and optimization. We have established a weak convergence result based on the assumption of the pseudomonotone property and a certain Lipschitz-type cost bifunctional condition. The stepsize, in this case, depends upon on the Lipschitz-type constants and the extrapolation factor. The bifunction is strongly pseudomonotone in the second method, but stepsize does not depend on the strongly pseudomonotone and Lipschitz-type constants. In contrast, the first convergence result, we set up strong convergence with the use of a variable stepsize sequence, which is decreasing and non-summable. As the application, the variational inequality problems that involve pseudomonotone and strongly pseudomonotone operator are considered. Finally, two well-known Nash–Cournot equilibrium models for the numerical experiment are reviewed to examine our convergence results and show the competitive advantage of our suggested methods.

Modified inertial subgradient extragradient method for equilibrium problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Yekini Shehu ◽  
Regina N. Nwokoye
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Weak And Strong Convergence ◽  
Extragradient Methods ◽  
Convergence Results ◽  
Inertial Extrapolation ◽  
Special Case

Abstract The subgradient extragradient method with inertial extrapolation step x n + θ n (x n − x n−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.

The subgradient extragradient method for pseudomonotone equilibrium problems

Optimization ◽  
2019 ◽  
Vol 69 (4) ◽  
pp. 901-923 ◽  
Author(s):  
Vahid Dadashi ◽  
Olaniyi S. Iyiola ◽  
Yekini Shehu
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method

scholarly journals A Parallel Hybrid Bregman Subgradient Extragradient Method for a System of Pseudomonotone Equilibrium and Fixed Point Problems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 216
Author(s):  
Annel Thembinkosi Bokodisa ◽  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Convergence Result ◽  
Point Problem ◽  
Subgradient Extragradient Method ◽  
Reflexive Banach Spaces ◽  
Common Fixed Point Problem ◽  
Parallel Hybrid

We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

The subgradient extragradient method extended to equilibrium problems

Optimization ◽  
2012 ◽  
Vol 64 (2) ◽  
pp. 225-248 ◽  
Author(s):  
Pham Ngoc Anh ◽  
Le Thi Hoai An
Keyword(s):  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method
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