Inertial subgradient projection techniques for solving a class of bilevel equilibrium problems

ABSTRACT

In this paper, we introduce a new algorithm for solving bilevel equilibrium problems with nonexpansive and pseudocontractive mappings in a real Hilbert space. The proposed algorithm is based on subgradient method with Armijo-type linesearch process, subgradient method, and inertial projection techniques. By choosing the suitable regular parameters, we prove strong convergence of the algorithm under classical conditions of the cost bifunctions.

KEYWORDS:

• Bilevel equilibrium problems
• subgradient
• projection method
• pseudomonotone
• Lipschitz continuous

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65K10
• 90C25
• 49J35
• 47J25

Acknowledgments

The authors would like to thank Professor Stephan Dempe -- the Associate Editor and the anonymous referees for their really helpful and constructive comments and suggestions that helped us very much in improving the paper. This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2023.01.

Disclosure statement

No potential conflict of interest was reported by the author(s).