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Clarke's Local Generalized Nash Equilibria with Nonconvex Coupling Constraints
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  • Paolo Scarabaggio ,
  • Raffaele Carli ,
  • Sergio Grammatico ,
  • Mariagrazia Dotoli
Paolo Scarabaggio
Politecnico di Bari, Politecnico di Bari

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Raffaele Carli
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Sergio Grammatico
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Mariagrazia Dotoli
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We consider a class of Nash games with nonconvex coupling constraints where we leverage the theory of tangent cones to define a novel notion of local equilibrium: Clarke’s local generalized Nash equilibrium (CL-GNE).
Our first technical contribution is to show the stability of these equilibria on a specific local subset of the original feasible set.
As a second contribution, we show that the proposed notion of local equilibrium can be equivalently formulated as the solution of a quasi-variational inequality, remarkably, with equal Lagrange multipliers.
Next, we define conditions for the existence and uniqueness of the CL-GNE.
To compute such an equilibrium, we propose two discrete-time distributed dynamics, or fixed-point iterations.
Our third technical contribution is to  prove convergence under (strongly) monotone assumptions on the pseudo-gradient mapping of the game.
Finally, we apply our theoretical results to a competitive version of the optimal power flow control problem.
Paper submitted for publication in IEEE Transactions on Automatic Control – http://ieeecss.org/publication/transactions-automatic-control