An extragradient algorithm for a lifted reformulation of projected solutions for quasiequilibria

Projected solutions of a quasiequilibrium problem are shown to coincide with the (canonical) solutions of an auxiliary problem, that is obtained by doubling the variables and adding suitable penalty terms to the equilibrium bifunction. Unfortunately, the assumptions of existing algorithms for computing quasiequilibria are never met by this lifted reformulation due to its peculiar structure. Therefore, an ad-hoc version of the hyperplane extragradient algorithm is devised and its parameters are tuned appropriately to cope with the auxiliary problem. Finally, preliminary numerical results show the behaviour of the algorithm.