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

03/28/2018

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by   Giuseppe Belgioioso, et al.

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We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to 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 methods. More generally, we provide a unifying operator-theoretic ground to design projected-gradient methods for generalized equilibrium seeking in aggregative games.