In this paper, we investigate distributed generalized Nash equilibrium (GNE)computation of monotone games with affine coupling constraints. Each player canonly utilize its local objective function, local feasible set and a local blockof the coupling constraint, and can only communicate with its neighbours. Weassume the game has monotone pseudo-subdifferential without Lipschitzcontinuity restrictions. We design novel center-free distributed GNE seekingalgorithms for equality and inequality affine coupling constraints,respectively. A proximal alternating direction method of multipliers(ADMM) isproposed for the equality case, while for the inequality case, a parallelsplitting type algorithm is proposed. In both algorithms, the GNE seeking taskis decomposed into a sequential NE computation of regularized subgames anddistributed update of multipliers and auxiliary variables, based on local dataand local communication. Our two double-layer GNE algorithms need not specifythe inner-loop NE seeking algorithm and moreover, only require that thestrongly monotone subgames are inexactly solved. We prove their convergence byshowing that the two algorithms can be seen as specific instances ofpreconditioned proximal point algorithms} (PPPA) for finding zeros of monotoneoperators. Applications and numerical simulations are given for illustration.
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