A dynamical approach for bilevel equilibrium problems and its applications to control problems

In this paper, a forward–backward–forward method is employed for a dynamical system to solve the bilevel equilibrium problems over a real Hilbert space, and the convergence of the dynamic system's trajectory is established. Furthermore, quantitative stability analysis has been extensively studied for perturbed bilevel equilibrium problems by considering different metrics. As applications, stability analysis is derived for convex minimization problems and for optimal control problems where a variational inequality gives the state-control relation.