A general class of relative optimization problems

We consider relative or subjective optimization problems where the goal function and feasible set are dependent on current state of system under consideration. In general, they formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. describe a general class in metric spaces, which addition depend starting state. also utilize type formulations these show that admit simple descent solution methods. This approach gives suitable trajectories tending to relatively optimal several examples applications problems. Preliminary results computational experiments confirmed efficiency proposed method.