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We show that projected-gradient methods for the distributed computation ofgeneralized Nash equilibria in aggregative games are preconditionedforward-backward splitting methods applied to the KKT operator of the game.Specifically, we adopt the preconditioned forward-backward design, recentlyconceived by Yi and Pavel in the manuscript "A distributed primal-dualalgorithm for computation of generalized Nash equilibria via operator splittingmethods" for generalized Nash equilibrium seeking in aggregative games.Consequently, we notice that two projected-gradient methods recently proposedin the literature are preconditioned forward-backward methods. More generally,we provide a unifying operator-theoretic ground to design projected-gradientmethods for generalized equilibrium seeking in aggregative games.

Projected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods