Inertial subgradient-type algorithm for solving equilibrium problems with strong monotonicity over fixed point sets

This paper introduces an inertial subgradient-type algorithm for solving equilibrium problems with strong monotonicity, constrained over the fixed point set of a nonexpansive mapping in the framework of a real Hilbert space. The proposed method integrates inertial and subgradient strategies to enhance convergence properties while avoiding the computational challenges of metric projections onto complex sets. A strong convergence theorem is established under appropriate constraint qualifications for the scalar sequences. Numerical experiments in both finite and infinite dimensional settings, including applications to Nash-Cournot oligopolistic market equilibrium models, highlight the efficacy and computational advantages of the algorithm. These results demonstrate the potential for broader applications in optimization and variational analysis.