An Efficient Single Projection Scheme for Solving Bilevel Variational Inequality Problems: Application to Fractional Programming Problem

Abstract This research examines the bilevel monotone variational inequality problem and presents a novel single projection technique for finding solutions in Hilbert spaces. The proposed algorithm enhances convergence speed by incorporating inertial techniques and self-adaptive step sizes. Unlike conventional methods, this approach requires only one projection onto a half-space, thus reducing computational costs. The study demonstrates strong convergence results for the algorithm under moderate conditions on control parameters. Through various numerical experiments, the method’s efficacy is illustrated, highlighting its advantages. Furthermore, the research extends the application of this technique to tackle fractional programming problems.