Globally Convergent Algorithms for the Solution of Generalized Nash Equilibrium Problems

[1]  Masao Fukushima,et al.  Restricted generalized Nash equilibria and controlled penalty algorithm , 2011, Comput. Manag. Sci..

[2]  Xiaojun Chen,et al.  A penalized Fischer-Burmeister NCP-function , 2000, Math. Program..

[3]  J. Goodman Note on Existence and Uniqueness of Equilibrium Points for Concave N-Person Games , 1965 .

[4]  R. W. Chaney Piecewise functions in nonsmooth analysis , 1990 .

[5]  Stephan Dempe,et al.  Directional derivatives of the solution of a parametric nonlinear program , 1995, Math. Program..

[6]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[7]  Jong-Shi Pang,et al.  Piecewise Smoothness, Local Invertibility, and Parametric Analysis of Normal Maps , 1996, Math. Oper. Res..

[8]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[9]  Sjur Didrik Flåm,et al.  Noncooperative Convex Games: Computing Equilibrium by Partial Regularization , 1994 .

[10]  Francisco Facchinei,et al.  Nash equilibria: the variational approach , 2010, Convex Optimization in Signal Processing and Communications.

[11]  Christian Kanzow,et al.  Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions , 2009, Comput. Optim. Appl..

[12]  Francisco Facchinei,et al.  Partial penalization for the solution of generalized Nash equilibrium problems , 2011, J. Glob. Optim..

[13]  P. Harker Generalized Nash games and quasi-variational inequalities , 1991 .

[14]  Christian Kanzow,et al.  SC 1 optimization reformulations of the generalized Nash equilibrium problem , 2008, Optim. Methods Softw..

[15]  C. Kanzow,et al.  Relaxation Methods for Generalized Nash Equilibrium Problems with Inexact Line Search , 2009 .

[16]  H. Nikaidô,et al.  Note on non-cooperative convex game , 1955 .

[17]  Oliver Stein,et al.  Bi-Level Strategies in Semi-Infinite Programming , 2003 .

[18]  Francisco Facchinei,et al.  Penalty Methods for the Solution of Generalized Nash Equilibrium Problems , 2010, SIAM J. Optim..

[19]  Francisco Facchinei,et al.  Distributed Power Allocation With Rate Constraints in Gaussian Parallel Interference Channels , 2007, IEEE Transactions on Information Theory.

[20]  G. Tullock Efficient Rent Seeking , 2001 .

[21]  Andreas Fischer,et al.  On generalized Nash games and variational inequalities , 2007, Oper. Res. Lett..

[22]  Francisco Facchinei,et al.  Generalized Nash Equilibrium Problems , 2010, Ann. Oper. Res..

[23]  Tobias Scheffer,et al.  Nash Equilibria of Static Prediction Games , 2009, NIPS.

[24]  Francisco Facchinei,et al.  Generalized Nash equilibrium problems and Newton methods , 2008, Math. Program..

[25]  Masao Fukushima,et al.  Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games , 2009, Comput. Manag. Sci..

[26]  Hubertus Th. Jongen,et al.  On Structure and Computation of Generalized Nash Equilibria , 2013, SIAM J. Optim..

[27]  Renato D. C. Monteiro,et al.  A Potential Reduction Newton Method for Constrained Equations , 1999, SIAM J. Optim..

[28]  Masao Fukushima,et al.  A globalized Newton method for the computation of normalized Nash equilibria , 2013, J. Glob. Optim..

[29]  Masao Fukushima,et al.  Newton’s method for computing a normalized equilibrium in the generalized Nash game through fixed point formulation , 2012, Math. Program..

[30]  F. Facchinei,et al.  Hamburger Beitr Age Zur Angewandten Mathematik a Simply Constrained Optimization Reformulation of Kkt Systems Arising from Variational Inequalities Hamburger Beitr Age Zur Angewandten Mathematik Reihe a Preprints Reihe B Berichte Reihe C Mathematische Modelle Und Simulation Reihe D Elektrische Netzw , 1996 .

[31]  Masao Fukushima,et al.  Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints , 2011, Comput. Optim. Appl..

[32]  Luiz Carlos Matioli,et al.  A numerical algorithm for finding solutions of a generalized Nash equilibrium problem , 2012, Comput. Optim. Appl..

[33]  Gül Gürkan,et al.  Approximations of Nash equilibria , 2008, Math. Program..

[34]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[35]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[36]  Christian Kanzow,et al.  Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems , 2011, Comput. Optim. Appl..

[37]  Francisco Facchinei,et al.  Exact penalty functions for generalized Nash problems , 2006 .

[38]  Stefania Bellavia,et al.  STRSCNE: A Scaled Trust-Region Solver for Constrained Nonlinear Equations , 2004, Comput. Optim. Appl..

[39]  R. Janin Directional derivative of the marginal function in nonlinear programming , 1984 .

[40]  Stefania Bellavia,et al.  An affine scaling trust-region approach to bound-constrained nonlinear systems , 2003 .

[41]  Masao Fukushima,et al.  Gap Function Approach to the Generalized Nash Equilibrium Problem , 2010 .

[42]  Eleftherios Couzoudis,et al.  Computing generalized Nash equilibria by polynomial programming , 2013, Math. Methods Oper. Res..

[43]  Adrian S. Lewis,et al.  A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization , 2005, SIAM J. Optim..

[44]  Naihua Xiu,et al.  Some projection-like methods for the generalized Nash equilibria , 2010, Comput. Optim. Appl..

[45]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[46]  M. Fukushima A class of gap functions for quasi-variational inequality problems , 2007 .

[47]  Francisco Facchinei,et al.  A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm , 1997, SIAM J. Optim..

[48]  Francisco Facchinei,et al.  Regularity Properties of a Semismooth Reformulation of Variational Inequalities , 1998, SIAM J. Optim..

[49]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[50]  J. Nash,et al.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[51]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[52]  Francisco Facchinei,et al.  On the solution of the KKT conditions of generalized Nash equilibrium problems , 2011, SIAM J. Optim..

[53]  R. Rubinstein,et al.  On relaxation algorithms in computation of noncooperative equilibria , 1994, IEEE Trans. Autom. Control..

[54]  K. Taji,et al.  On Gap Functions for Quasi-Variational Inequalities , 2008 .

[55]  Francisco Facchinei,et al.  A semismooth equation approach to the solution of nonlinear complementarity problems , 1996, Math. Program..

[56]  A. Bensoussan Points de Nash Dans le Cas de Fonctionnelles Quadratiques et Jeux Differentiels lineaires a N Personnes , 1974 .

[57]  Stan Uryasev,et al.  Relaxation algorithms to find Nash equilibria with economic applications , 2000 .

[58]  W. Hogan Point-to-Set Maps in Mathematical Programming , 1973 .

[59]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[60]  Francisco Facchinei,et al.  A Theoretical and Numerical Comparison of Some Semismooth Algorithms for Complementarity Problems , 2000, Comput. Optim. Appl..

[61]  Francisco Facchinei,et al.  Decomposition algorithms for generalized potential games , 2011, Comput. Optim. Appl..

[62]  Masao Fukushima,et al.  Solving box constrained variational inequalities by using the natural residual with D-gap function globalization , 1998, Oper. Res. Lett..

[63]  Liqun Qi,et al.  A nonsmooth version of Newton's method , 1993, Math. Program..

[64]  Oliver Stein,et al.  Nonsmooth optimization reformulations of player convex generalized Nash equilibrium problems , 2012, J. Glob. Optim..