Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces

Abstract

The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost operator is not required. Under appropriate conditions, the strong convergence of the algorithms is established. We also present several numerical experiments which bring out the efficiency and the advantages of the proposed algorithms. Our work provides extensions of many known results from Hilbert spaces to reflexive Banach spaces.

Keywords:

• Bregman projection
• extragradient method
• Legendre function
• reflexive banach space
• strong convergence

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 47H09
• 47H10
• 47J25
• 47J05

Additional information

Funding

Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. P. Cholamjiak was supported by University of Phayao and Thailand Science Research and Innovation grant no. FF65-UoE001. All the authors are very grateful to the editor and to the anonymous referees for their valuable comments and pertinent suggestions.