On Subgradient Extragradient Rule with Inertial Correction for Bilevel Pseudomonotone VIP with Constraints of Equilibria System and Split CFPP

Abstract

In this paper, let the BPVIP, GEPS, and SCFPP represent a bilevel pseudomonotone variational inequality problem, a generalized equilibrium problems system, and a split common fixed point problem involving demimetric mappings in real Hilbert spaces, respectively. We devise a composite subgradient extragradient rule with an inertial correction term for
solving the BPVIP with constraints of GEPS and SCFPP, where the rule exploits the inertial technique with a correction term and a self-adaptive stepsize strategy. The BPVIP consists of the upper-level VIP for one strongly monotone operator and the lower-level VIP for another pseudomonotone operator. The strong convergence result for the designed algorithm is
established under certain suitable conditions. In addition, the main result is employed to handle a bilevel split pseudomonotone variational inequality problem (BSPVIP). Lastly, an illustrated instance is utilized to back up the applicability and performability of the suggested rule.