Alternated inertial subgradient extragradient method for equilibrium problems

Yekini Shehu ^[1] ; Qiao-Li Dong ^[3] ; Lulu Liu ^[3] ; Jen-Chih Yao ^[2]
1. [1] Zhejiang Normal University
  
  Zhejiang Normal University
  
  China
2. [2] China Medical University
  
  China Medical University
  
  Taiwán
3. [3] Civil Aviation University of China, China
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Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 31, Nº. 1, 2023, págs. 1-30
Idioma: inglés
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Resumen
- The focus of this paper is to obtain weak and linear convergence analysis of the subgradient extragradient method with alternated inertial step for solving equilibrium problems in real Hilbert spaces. The proposed method uses self-adaptive step sizes. Weak convergence is established without Lipschitz constant of the bifunction as an input parameter. Linear convergence is obtained without the modulus of strong pseudomonotonicity and Lipschitz constant as input parameters. We report some priori and posteriori error estimates and some numerical experiments to illustrate the behavior of our proposed method with related methods.