Theoretical and numerical aspects of projected solution for quasiequilibrium problems

Most of the results concerning the existence of quasiequilibrium problems require the constraint map to be a self-map. However, in some applications, the constraint map may not be a self-map. Aussel, Sultana, and Vetrivel [4] introduced the concept of projected solution for quasivariational inequalities and generalized Nash equilibria to address this issue. Cotrina and Zúñiga [27] later adapted this concept to quasiequilibrium problems. This thesis examines an electricity market model that leads to a generalized equilibrium problem in which a constraint map cannot be a self-map. The thesis then presents an existence result for projected solutions [20] in the finite dimensional setting. This is achieved without any monotonicity assumptions and without requiring the compactness of the feasible set. Additionally, we establish the existence of projected solutions for quasivariational inequalities, quasioptimization problems, and generalized Nash equilibrium problems. Finally, we illustrate an iterative procedure for discovering a projected solution. The proposed method is founded on the concept of a gap function and a reformulation of the quasiequilibrium problem as a global optimization problem.