On a threshold descent method for quasi-equilibria

We describe a special class of quasi-equilibrium problems in metric spaces and propose a novel simple threshold descent method for solving these problems. Due to the framework, the convergence of the method cannot be established with the usual convexity or generalized convexity assumptions. Under mild conditions, the iterative procedure gives solutions of the quasi-equilibrium problem. We apply this method to scalar and vector generalized quasi-equilibrium problems and to some classes of relative optimization problems.