An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems

Shehu Y, Iyiola OS, Thong DV, Van NTC. 2020. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research.

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Journal Article | Epub ahead of print | English

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Author
Shehu, YekiniIST Austria ; Iyiola, Olaniyi S.; Thong, Duong Viet; Van, Nguyen Thi Cam
Department
Abstract
The paper introduces an inertial extragradient subgradient method with self-adaptive step sizes for solving equilibrium problems in real Hilbert spaces. Weak convergence of the proposed method is obtained under the condition that the bifunction is pseudomonotone and Lipchitz continuous. Linear convergence is also given when the bifunction is strongly pseudomonotone and Lipchitz continuous. Numerical implementations and comparisons with other related inertial methods are given using test problems including a real-world application to Nash–Cournot oligopolistic electricity market equilibrium model.
Publishing Year
Date Published
2020-11-18
Journal Title
Mathematical Methods of Operations Research
Acknowledgement
The authors are grateful to the two referees and the Associate Editor for their comments and suggestions which have improved the earlier version of the paper greatly. The project of Yekini Shehu has received funding from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7 - 2007-2013) (Grant agreement No. 616160).
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Shehu Y, Iyiola OS, Thong DV, Van NTC. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. 2020. doi:10.1007/s00186-020-00730-w
Shehu, Y., Iyiola, O. S., Thong, D. V., & Van, N. T. C. (2020). An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research. Springer Nature. https://doi.org/10.1007/s00186-020-00730-w
Shehu, Yekini, Olaniyi S. Iyiola, Duong Viet Thong, and Nguyen Thi Cam Van. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research. Springer Nature, 2020. https://doi.org/10.1007/s00186-020-00730-w.
Y. Shehu, O. S. Iyiola, D. V. Thong, and N. T. C. Van, “An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems,” Mathematical Methods of Operations Research. Springer Nature, 2020.
Shehu Y, Iyiola OS, Thong DV, Van NTC. 2020. An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems. Mathematical Methods of Operations Research.
Shehu, Yekini, et al. “An Inertial Subgradient Extragradient Algorithm Extended to Pseudomonotone Equilibrium Problems.” Mathematical Methods of Operations Research, Springer Nature, 2020, doi:10.1007/s00186-020-00730-w.

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