Distributed algorithms for the computation of noncooperative equilibria
Automatica (Journal of IFAC)
Mathematical Programming: Series A and B
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
Unconstrained optimization reformulations of variational inequality problems
Journal of Optimization Theory and Applications
Equilibrium programming using proximal-like algorithms
Mathematical Programming: Series A and B
Equivalence of variational inequality problems to unconstrained minimization
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
The Barzilai and Borwein Gradient Method for the Large Scale Unconstrained Minimization Problem
SIAM Journal on Optimization
Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method
Computational Optimization and Applications
Gap Functions for Equilibrium Problems
Journal of Global Optimization
Approximations of Nash equilibria
Mathematical Programming: Series A and B
Generalized Nash equilibrium problems and Newton methods
Mathematical Programming: Series A and B
Game-Theoretic analysis of internet switching with selfish users
WINE'05 Proceedings of the First international conference on Internet and Network Economics
On generalized Nash games and variational inequalities
Operations Research Letters
SC1 optimization reformulations of the generalized Nash equilibrium problem
Optimization Methods & Software
Some projection-like methods for the generalized Nash equilibria
Computational Optimization and Applications
Penalty Methods for the Solution of Generalized Nash Equilibrium Problems
SIAM Journal on Optimization
SIAM Journal on Optimization
Computational Optimization and Applications
Computational Optimization and Applications
Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems
Journal of Global Optimization
Gap functions and penalization for solving equilibrium problems with nonlinear constraints
Computational Optimization and Applications
Interior point methods for equilibrium problems
Computational Optimization and Applications
A globalized Newton method for the computation of normalized Nash equilibria
Journal of Global Optimization
Hi-index | 0.00 |
We consider the generalized Nash equilibrium problem which, in contrast to the standard Nash equilibrium problem, allows joint constraints of all players involved in the game. Using a regularized Nikaido-Isoda-function, we then present three optimization problems related to the generalized Nash equilibrium problem. The first optimization problem is a complete reformulation of the generalized Nash game in the sense that the global minima are precisely the solutions of the game. However, this reformulation is nonsmooth. We then modify this approach and obtain a smooth constrained optimization problem whose global minima correspond to so-called normalized Nash equilibria. The third approach uses the difference of two regularized Nikaido-Isoda-functions in order to get a smooth unconstrained optimization problem whose global minima are, once again, precisely the normalized Nash equilibria. Conditions for stationary points to be global minima of the two smooth optimization problems are also given. Some numerical results illustrate the behaviour of our approaches.