Projected-gradient algorithms for generalized equilibrium seeking in aggregative games are preconditioned forward-backward methods

We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in ag- gregative games are preconditioned forward-backward splitting methods appliedto the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript ’’A distributed primal-dual algorithm for computation of generalized Nash equilibria via operator splitting methods’’ for generalized Nash equilibrium seeking in aggregative games. Consequently, we notice that two projected-gradient methods recently proposed in the literature are preconditioned forward-backward meth- ods. More generally, we provide a unifying operator-theoretic ground to design projected-gradient methods for generalized equilibrium seeking in aggregative games.