Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality

Abstract

Abstract This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The problem under consideration is in real Hilbert spaces, where the BSPVIP involves a fixed point problem of demimetric mapping. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under some suitable assumptions. In addition, a numerical example is given to demonstrate the viability of the proposed rule. Our results improve and extend some recent developments to a great extent.

Keywords

• Subgradient extragradient process
• Bilevel split pseudomonotone variational inequality problem
• Extrapolation step
• Demimetric mapping
• Fixed point
• Nonexpansive mapping