THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES

doi:10.1007/s10473-025-0423-0

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1674-1700.doi: 10.1007/s10473-025-0423-0

THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES

Yonghong YAO^1,2,3, Olaniyi S. IYIOLA⁴, Yekini SHEHU^5,*

1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China;
2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, China;
3. Center for Advanced Information Technology, Kyung Hee University, Seoul 02447, South Korea;
4. Department of Mathematics, Morgan State University, Baltimore, MD, USA;
5. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2024-03-12 修回日期:2024-10-31 出版日期:2025-10-10 发布日期:2025-10-10

THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES

Yonghong YAO^1,2,3, Olaniyi S. IYIOLA⁴, Yekini SHEHU^5,*

1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China;
2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan, China;
3. Center for Advanced Information Technology, Kyung Hee University, Seoul 02447, South Korea;
4. Department of Mathematics, Morgan State University, Baltimore, MD, USA;
5. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Received:2024-03-12 Revised:2024-10-31 Online:2025-10-10 Published:2025-10-10
Contact: ^*Yekini SHEHU, E-mail: yekini.shehu@zjnu.edu.cn; deltanougt2006@yahoo.com
About author:Yonghong YAO, E-mail: yyhtgu@hotmail.com; Olaniyi S. IYIOLA, E-mail: niyi4oau@gmail.com; olaniyi.iyiola@morgan.edu

摘要/Abstract

摘要： Several results on iterative methods for equilibrium problems have been proposed and studied in the literature. Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator. Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature. In this paper, we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity. We propose two weakly convergent iterative algorithms and one strongly convergent algorithm. We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction. Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.

关键词: equilibrium problem, nonmonotone bifunction, weak convergence, strong convergence

Abstract: Several results on iterative methods for equilibrium problems have been proposed and studied in the literature. Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator. Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature. In this paper, we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity. We propose two weakly convergent iterative algorithms and one strongly convergent algorithm. We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction. Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.

Key words: equilibrium problem, nonmonotone bifunction, weak convergence, strong convergence

Yonghong YAO, Olaniyi S. IYIOLA, Yekini SHEHU. THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES[J]. 数学物理学报(英文版), 2025, 45(4): 1674-1700.

Yonghong YAO, Olaniyi S. IYIOLA, Yekini SHEHU. THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1674-1700.

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THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES

THREE INERTIAL ACCELERATION ALGORITHMS FOR SOLVING NON-MONOTONE EQUILIBRIUM PROBLEMS IN HILBERT SPACES

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