Extragradient subgradient methods for solving bilevel equilibrium problems

Abstract

Abstract In this paper, we propose two algorithms for finding the solution of a bilevel equilibrium problem in a real Hilbert space. Under some sufficient assumptions on the bifunctions involving pseudomonotone and Lipschitz-type conditions, we obtain the strong convergence of the iterative sequence generated by the first algorithm. Furthermore, the strong convergence of the sequence generated by the second algorithm is obtained without a Lipschitz-type condition.

Keywords

• Bilevel equilibrium problems
• Extragradient Subgradient-Halpern methods
• Armijo line search
• Strong convergence