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A penalty method for generalized Nash equilibrium problems
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China, China, China |
References:
[1] |
K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy,, Econometrica, 22 (1954), 265.
doi: 10.2307/1907353. |
[2] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods,", Athena Scientific, (1996). Google Scholar |
[3] |
B. Chen, X. Chen and C. Kanzow, A penalized Fischer-Burmeister NCP-function,, Mathematical Programming, 88 (2000), 211.
doi: 10.1007/PL00011375. |
[4] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", John Wiley & Sons, (1983). Google Scholar |
[5] |
G. Debreu, Definite and semidefinite quadratic forms,, Econometrica, 20 (1952), 295.
doi: 10.2307/1907852. |
[6] |
F. Facchinei, A. Fischer and V. Piccialli, Generalized Nash equilibrium problems and Newton methods,, Mathematical Programming, 117 (2009), 163.
doi: 10.1007/s10107-007-0160-2. |
[7] |
F. Facchinei and C. Kanzow, Penalty methods for the solution of generalized nash equilibrium problems,, SIAM Journal on Optimization, 20 (2010), 2228.
doi: 10.1137/090749499. |
[8] |
F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, Annals of Operations Research, 175 (2010), 177.
doi: 10.1007/s10479-009-0653-x. |
[9] |
M. Fukushima, Restricted generalized Nash equilibria and controlled penalty algorithm,, Technical Report 2008-007, (2008), 2008. Google Scholar |
[10] |
A. Heusinger and C. Kanzow, Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type funcitons,, Computational Optimization and Applications, 43 (2009), 353.
doi: 10.1007/s10589-007-9145-6. |
[11] |
A. Kesselman, S. Leonardi and V. Bonifaci, Game-theoretic analysis of internet switching with selfish users,, Lecture Notes in Computer Science, 3828 (2005), 236.
doi: 10.1007/11600930_23. |
[12] |
R. Mifflin, Semismooth and semiconvex functions in constrained optimization,, SIAM Journal on Control and Optimization, 15 (1977), 959.
doi: 10.1137/0315061. |
[13] |
L. W. McKenzie, On the existence of a general equilibrium for a competitive market,, Econometrica, 27 (1959), 54.
doi: 10.2307/1907777. |
[14] |
J. F. Nash, Jr., Equilibrium points in $n$-person games,, Proceedings of the National Academy of Sciences of the USA, 36 (1950), 48.
doi: 10.1073/pnas.36.1.48. |
[15] |
J. F. Nash, Non-cooperative games,, Annals of Mathematics (2), 54 (1951), 286.
doi: 10.2307/1969529. |
[16] |
J. V. Neumann, Zur theorie der gesellschaftsspiele,, Mathematische Annalen, 100 (1928), 295.
doi: 10.1007/BF01448847. |
[17] |
J. V. Neumann and O. Morgenstern, "Theory of Games and Economic Behavior,", Princeton University Press, (1953). Google Scholar |
[18] |
J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games,, Computational Management Science, 2 (2005), 21.
doi: 10.1007/s10287-004-0010-0. |
[19] |
L. Qi and J. Sun, A nonsmooth version of Newton's method,, Mathematical Programming, 58 (1993), 353.
doi: 10.1007/BF01581275. |
[20] |
L. Qi, D. Sun and G. Zhou, A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities,, Mathematical Programming, 87 (2000), 1.
|
[21] |
J. B. Rosen, Existence and uniqueness of equilibrium points for concave $n$-person games,, Econometrica, 33 (1965), 520.
doi: 10.2307/1911749. |
[22] |
D. Sun, The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications,, Mathematics of Operations Research, 31 (2006), 761.
doi: 10.1287/moor.1060.0195. |
[23] |
J. Sun, D. Sun and L. Qi, A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems,, SIAM Journal on Optimization, 14 (2004), 783.
doi: 10.1137/S1052623400379620. |
show all references
References:
[1] |
K. J. Arrow and G. Debreu, Existence of an equilibrium for a competitive economy,, Econometrica, 22 (1954), 265.
doi: 10.2307/1907353. |
[2] |
D. P. Bertsekas, "Constrained Optimization and Lagrange Multiplier Methods,", Athena Scientific, (1996). Google Scholar |
[3] |
B. Chen, X. Chen and C. Kanzow, A penalized Fischer-Burmeister NCP-function,, Mathematical Programming, 88 (2000), 211.
doi: 10.1007/PL00011375. |
[4] |
F. H. Clarke, "Optimization and Nonsmooth Analysis,", John Wiley & Sons, (1983). Google Scholar |
[5] |
G. Debreu, Definite and semidefinite quadratic forms,, Econometrica, 20 (1952), 295.
doi: 10.2307/1907852. |
[6] |
F. Facchinei, A. Fischer and V. Piccialli, Generalized Nash equilibrium problems and Newton methods,, Mathematical Programming, 117 (2009), 163.
doi: 10.1007/s10107-007-0160-2. |
[7] |
F. Facchinei and C. Kanzow, Penalty methods for the solution of generalized nash equilibrium problems,, SIAM Journal on Optimization, 20 (2010), 2228.
doi: 10.1137/090749499. |
[8] |
F. Facchinei and C. Kanzow, Generalized Nash equilibrium problems,, Annals of Operations Research, 175 (2010), 177.
doi: 10.1007/s10479-009-0653-x. |
[9] |
M. Fukushima, Restricted generalized Nash equilibria and controlled penalty algorithm,, Technical Report 2008-007, (2008), 2008. Google Scholar |
[10] |
A. Heusinger and C. Kanzow, Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type funcitons,, Computational Optimization and Applications, 43 (2009), 353.
doi: 10.1007/s10589-007-9145-6. |
[11] |
A. Kesselman, S. Leonardi and V. Bonifaci, Game-theoretic analysis of internet switching with selfish users,, Lecture Notes in Computer Science, 3828 (2005), 236.
doi: 10.1007/11600930_23. |
[12] |
R. Mifflin, Semismooth and semiconvex functions in constrained optimization,, SIAM Journal on Control and Optimization, 15 (1977), 959.
doi: 10.1137/0315061. |
[13] |
L. W. McKenzie, On the existence of a general equilibrium for a competitive market,, Econometrica, 27 (1959), 54.
doi: 10.2307/1907777. |
[14] |
J. F. Nash, Jr., Equilibrium points in $n$-person games,, Proceedings of the National Academy of Sciences of the USA, 36 (1950), 48.
doi: 10.1073/pnas.36.1.48. |
[15] |
J. F. Nash, Non-cooperative games,, Annals of Mathematics (2), 54 (1951), 286.
doi: 10.2307/1969529. |
[16] |
J. V. Neumann, Zur theorie der gesellschaftsspiele,, Mathematische Annalen, 100 (1928), 295.
doi: 10.1007/BF01448847. |
[17] |
J. V. Neumann and O. Morgenstern, "Theory of Games and Economic Behavior,", Princeton University Press, (1953). Google Scholar |
[18] |
J.-S. Pang and M. Fukushima, Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games,, Computational Management Science, 2 (2005), 21.
doi: 10.1007/s10287-004-0010-0. |
[19] |
L. Qi and J. Sun, A nonsmooth version of Newton's method,, Mathematical Programming, 58 (1993), 353.
doi: 10.1007/BF01581275. |
[20] |
L. Qi, D. Sun and G. Zhou, A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities,, Mathematical Programming, 87 (2000), 1.
|
[21] |
J. B. Rosen, Existence and uniqueness of equilibrium points for concave $n$-person games,, Econometrica, 33 (1965), 520.
doi: 10.2307/1911749. |
[22] |
D. Sun, The strong second order sufficient condition and constraint nondegeneracy in nonlinear semidefinite programming and their implications,, Mathematics of Operations Research, 31 (2006), 761.
doi: 10.1287/moor.1060.0195. |
[23] |
J. Sun, D. Sun and L. Qi, A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems,, SIAM Journal on Optimization, 14 (2004), 783.
doi: 10.1137/S1052623400379620. |
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