Implicit functions and sensitivity of stationary points
Mathematical Programming: Series A and B
Piecewise functions in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications
Directional derivatives of the solution of a parametric nonlinear program
Mathematical Programming: Series A and B
Piecewise smoothness, local invertibility, and parametric analysis of normal maps
Mathematics of Operations Research
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
SIAM Journal on Optimization
Approximations of Nash equilibria
Mathematical Programming: Series A and B
Generalized Nash equilibrium problems and Newton methods
Mathematical Programming: Series A and B
SC1 optimization reformulations of the generalized Nash equilibrium problem
Optimization Methods & Software
Computational Optimization and Applications
Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems
Journal of Global Optimization
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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.