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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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Abstract

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.
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.