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

Habib ur Rehman, Poom Kumam, Meshal Shutaywi, Nasser Aedh Alreshidi and Wiyada Kumam
Additional contact information
Habib ur Rehman: KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Poom Kumam: KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Meshal Shutaywi: Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia
Nasser Aedh Alreshidi: Department of Mathematics, College of Science, Northern Border University, Arar 73222, Saudi Arabia
Wiyada Kumam: Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110, Thailand

Energies, 2020, vol. 13, issue 12, 1-28

Abstract: 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.

Keywords: energy production models; optimization problems; control parameters; Lipschitz-type conditions; variational inequality; Nash-Cournot oligopolistic equilibrium model (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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