A General Inertial Projection-Type Algorithm for Solving Equilibrium Problem in Hilbert Spaces with Applications in Fixed-Point Problems

A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introdu...

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Bibliographic Details
Published in:Axioms Vol. 9; no. 3; p. 101
Main Authors: Wairojjana, Nopparat, Rehman, Habib ur, De la Sen, Manuel, Pakkaranang, Nuttapol
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.09.2020
Subjects:
Algorithms
convex optimization
Equilibrium
equilibrium problems
fixed point problems
Fixed points (mathematics)
Hilbert space
Iterative methods
Mathematical analysis
Mathematical programming
Methods
Minimax technique
Optimization
pseudomonotone bifunction
variational inequality problems
weak convergence
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:A plethora of applications from mathematical programming, such as minimax, and mathematical programming, penalization, fixed point to mention a few can be framed as equilibrium problems. Most of the techniques for solving such problems involve iterative methods that is why, in this paper, we introduced a new extragradient-like method to solve equilibrium problems in real Hilbert spaces with a Lipschitz-type condition on a bifunction. The advantage of a method is a variable stepsize formula that is updated on each iteration based on the previous iterations. The method also operates without the previous information of the Lipschitz-type constants. The weak convergence of the method is established by taking mild conditions on a bifunction. For application, fixed-point theorems that involve strict pseudocontraction and results for pseudomonotone variational inequalities are studied. We have reported various numerical results to show the numerical behaviour of the proposed method and correlate it with existing ones.
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ISSN:2075-1680
2075-1680
DOI:10.3390/axioms9030101