Fast generalized Nash equilibrium seeking under partial-decision information

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all agents. The few existing methods build on projected pseudo-gradient dynamics, and require either double-layer iterations or conservative conditions on the step sizes. To overcome both these flaws and improve efficiency, we design the first fully-distributed single-layer algorithms based on proximal best-response. Our schemes are fixed-step and allow for inexact updates, which is crucial for reducing the computational complexity. Under standard assumptions on the game primitives, we establish convergence to a variational equilibrium (with linear rate for games without coupling constraints) by recasting our algorithms as proximal-point methods, opportunely preconditioned to distribute the computation among the agents. Besides, our operator-theoretic approach favors the implementation of provably correct acceleration schemes that can further improve the convergence speed. Since our analysis hinge on a restricted monotonicity property, we also provide new general results that significantly extend the domain of applicability of proximal-point methods. The potential of our algorithms is validated numerically, revealing much faster convergence with respect to the known projected pseudo-gradient algorithms.