Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems |
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Authors: | Axel Dreves Christian Kanzow |
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Institution: | 1.Institute of Mathematics,University of Würzburg,Würzburg,Germany |
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Abstract: | Generalized Nash equilibrium problems (GNEPs) allow, in contrast to standard Nash equilibrium problems, a dependence of the
strategy space of one player from the decisions of the other players. In this paper, we consider jointly convex GNEPs which
form an important subclass of the general GNEPs. Based on a regularized Nikaido-Isoda function, we present two (nonsmooth)
reformulations of this class of GNEPs, one reformulation being a constrained optimization problem and the other one being
an unconstrained optimization problem. While most approaches in the literature compute only a so-called normalized Nash equilibrium,
which is a subset of all solutions, our two approaches have the property that their minima characterize the set of all solutions
of a GNEP. We also investigate the smoothness properties of our two optimization problems and show that both problems are
continuous under a Slater-type condition and, in fact, piecewise continuously differentiable under the constant rank constraint
qualification. Finally, we present some numerical results based on our unconstrained optimization reformulation. |
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