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Volumn 43, Issue 3, 2009, Pages 353-377

Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions

Author keywords

Constrained optimization reformulation; Generalized Nash equilibria; Joint constraints; Normalized Nash equilibria; Regularized Nikaido Isoda function; Unconstrained optimization reformulation

Indexed keywords

CONSTRAINED OPTIMIZATION REFORMULATION; GENERALIZED NASH EQUILIBRIA; JOINT CONSTRAINTS; NORMALIZED NASH EQUILIBRIA; REGULARIZED NIKAIDO-ISODA-FUNCTION; UNCONSTRAINED OPTIMIZATION REFORMULATION;

EID: 67651018689     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9145-6     Document Type: Article
Times cited : (127)

References (38)
  • 3
    • 38249035395 scopus 로고
    • Relaxation techniques and asynchronous algorithms for on-line computation of non-cooperative equilibria
    • T. Başar 1987 Relaxation techniques and asynchronous algorithms for on-line computation of non-cooperative equilibria J. Econ. Dyn. Control 11 531 549
    • (1987) J. Econ. Dyn. Control , vol.11 , pp. 531-549
    • Başar, T.1
  • 5
    • 0001475203 scopus 로고
    • Points de Nash dans le cas de fonctionelles quadratiques et jeux differentiels lineaires a N personnes
    • A. Bensoussan 1974 Points de Nash dans le cas de fonctionelles quadratiques et jeux differentiels lineaires a N personnes SIAM J. Control 12 460 499
    • (1974) SIAM J. Control , vol.12 , pp. 460-499
    • Bensoussan, A.1
  • 6
    • 1442339029 scopus 로고    scopus 로고
    • Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets
    • J. Contreras M. Klusch J.B. Krawczyk 2004 Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets IEEE Trans. Power Syst. 19 195 206
    • (2004) IEEE Trans. Power Syst. , vol.19 , pp. 195-206
    • Contreras, J.1    Klusch, M.2    Krawczyk, J.B.3
  • 7
    • 0036102376 scopus 로고    scopus 로고
    • R-linear convergence of the Barzilai and Borwein gradient method
    • Y.H. Dai L.Z. Liao 2002 R-linear convergence of the Barzilai and Borwein gradient method IMA J. Numer. Anal. 22 1 10
    • (2002) IMA J. Numer. Anal. , vol.22 , pp. 1-10
    • Dai, Y.H.1    Liao, L.Z.2
  • 10
    • 33847081240 scopus 로고    scopus 로고
    • On generalized Nash games and variational inequalities
    • DOI 10.1016/j.orl.2006.03.004, PII S0167637706000484
    • F. Facchinei A. Fischer V. Piccialli 2007 On generalized Nash games and variational inequalities Oper. Res. Lett. 35 159 164 (Pubitemid 46275123)
    • (2007) Operations Research Letters , vol.35 , Issue.2 , pp. 159-164
    • Facchinei, F.1    Fischer, A.2    Piccialli, V.3
  • 11
    • 46749142109 scopus 로고    scopus 로고
    • Generalized Nash equilibrium problems and Newton methods
    • 10.1007/s10107-007-0160-2
    • F. Facchinei A. Fischer V. Piccialli 2007 Generalized Nash equilibrium problems and Newton methods Math. Program. Ser. B 10.1007/s10107-007-0160-2
    • (2007) Math. Program. Ser. B
    • Facchinei, F.1    Fischer, A.2    Piccialli, V.3
  • 12
    • 0039325157 scopus 로고    scopus 로고
    • Equilibrium programming using proximal-like algorithms
    • PII S0025561096000718
    • S.D. Flåm A.S. Antipin 1997 Equilibrium programming using proximal-like algorithms Math. Program. 78 29 41 (Pubitemid 127372132)
    • (1997) Mathematical Programming, Series B , vol.78 , Issue.1 , pp. 29-41
    • Flam, S.D.1    Antipin, A.S.2
  • 14
    • 0011768018 scopus 로고    scopus 로고
    • Department of Mathematics, University of Dundee, Dundee, United Kingdom, Numerical Analysis Report NA/207
    • Fletcher, R.: On the Barzilai-Borwein method. Department of Mathematics, University of Dundee, Dundee, United Kingdom, Numerical Analysis Report NA/207 (2001)
    • (2001) On the Barzilai-Borwein Method
    • Fletcher, R.1
  • 15
    • 0026763569 scopus 로고
    • Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
    • M. Fukushima 1992 Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems Math. Program. 53 99 110
    • (1992) Math. Program. , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 16
    • 0036853835 scopus 로고    scopus 로고
    • Nonmonotone globalization techniques for the Barzilai-Borwein gradient method
    • DOI 10.1023/A:1020587701058
    • L. Grippo M. Sciandrone 2002 Nonmonotone globalization techniques for the Barzilai-Borwein gradient method Comput. Optim. Appl. 23 143 169 (Pubitemid 35377442)
    • (2002) Computational Optimization and Applications , vol.23 , Issue.2 , pp. 143-169
    • Grippo, L.1    Sciandrone, M.2
  • 17
    • 46749133536 scopus 로고    scopus 로고
    • Approximations of Nash equilibria
    • 10.1007/s10107-007-0156-y
    • G. Gürkan J.-S. Pang 2007 Approximations of Nash equilibria Math. Program. Ser. B 10.1007/s10107-007-0156-y
    • (2007) Math. Program. Ser. B
    • Gürkan, G.1    Pang, J.-S.2
  • 18
    • 0026417165 scopus 로고
    • Generalized Nash games and quasivariational inequalities
    • P.T. Harker 1991 Generalized Nash games and quasivariational inequalities Eur. J. Oper. Res. 54 81 94
    • (1991) Eur. J. Oper. Res. , vol.54 , pp. 81-94
    • Harker, P.T.1
  • 19
    • 0035340070 scopus 로고    scopus 로고
    • Linear complementarity models of nash-Cournot competition in bilateral and POOLCO power markets
    • DOI 10.1109/59.918286, PII S0885895001037816
    • B.F. Hobbs 2001 Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets IEEE Trans. Power Syst. 16 194 202 (Pubitemid 32444276)
    • (2001) IEEE Transactions on Power Systems , vol.16 , Issue.2 , pp. 194-202
    • Hobbs, B.F.1
  • 20
    • 0001683067 scopus 로고
    • Point-to-set maps in mathematical programming
    • W.W. Hogan 1973 Point-to-set maps in mathematical programming SIAM Rev. 15 591 603
    • (1973) SIAM Rev. , vol.15 , pp. 591-603
    • Hogan, W.W.1
  • 21
    • 0002222760 scopus 로고    scopus 로고
    • Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
    • PII S0025561097000658
    • C. Kanzow M. Fukushima 1998 Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities Math. Program. 83 55 87 (Pubitemid 128431380)
    • (1998) Mathematical Programming, Series B , vol.83 , Issue.1 , pp. 55-87
    • Kanzow, C.1    Fukushima, M.2
  • 23
    • 18144368863 scopus 로고    scopus 로고
    • Coupled constraint Nash equilibria in environmental games
    • DOI 10.1016/j.reseneeco.2004.08.001, PII S0928765504000661
    • J.B. Krawczyk 2005 Coupled constraint Nash equilibria in environmental games Resour. Energy Econ. 27 157 181 (Pubitemid 40621220)
    • (2005) Resource and Energy Economics , vol.27 , Issue.2 , pp. 157-181
    • Krawczyk, J.B.1
  • 24
    • 0034406492 scopus 로고    scopus 로고
    • Relaxation algorithms to find Nash equilibria with economic applications
    • J.B. Krawczyk S. Uryasev 2000 Relaxation algorithms to find Nash equilibria with economic applications Environ. Model. Assess. 5 63 73
    • (2000) Environ. Model. Assess. , vol.5 , pp. 63-73
    • Krawczyk, J.B.1    Uryasev, S.2
  • 25
    • 0023382715 scopus 로고
    • DISTRIBUTED ALGORITHMS FOR THE COMPUTATION OF NONCOOPERATIVE EQUILIBRIA.
    • DOI 10.1016/0005-1098(87)90081-1
    • S. Li T. Başar 1987 Distributed algorithms for the computation of noncooperative equilibria Automatica 23 523 533 (Pubitemid 17637293)
    • (1987) Automatica , vol.23 , Issue.4 , pp. 523-533
    • Li Shu1    Basar Tamer2
  • 26
    • 0242653626 scopus 로고    scopus 로고
    • Gap functions for equilibrium problems
    • G. Mastroeni 2003 Gap functions for equilibrium problems J. Global Optim. 27 411 426
    • (2003) J. Global Optim. , vol.27 , pp. 411-426
    • Mastroeni, G.1
  • 27
    • 84972517905 scopus 로고
    • Note on noncooperative convex games
    • H. Nikaido K. Isoda 1955 Note on noncooperative convex games Pac. J. Math. 5 807 815
    • (1955) Pac. J. Math. , vol.5 , pp. 807-815
    • Nikaido, H.1    Isoda, K.2
  • 28
    • 20444502586 scopus 로고    scopus 로고
    • Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
    • DOI 10.1007/s10287-004-0010-0
    • J.-S. Pang M. Fukushima 2005 Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games Comput. Manag. Sci. 2 21 56 (Pubitemid 40814996)
    • (2005) Computational Management Science , vol.2 , Issue.1 , pp. 21-56
    • Pang, J.-S.1    Fukushima, M.2
  • 29
    • 0003317924 scopus 로고
    • Nonsmooth equations: Motivation and algorithms
    • J.-S. Pang L. Qi 1993 Nonsmooth equations: motivation and algorithms SIAM J. Optim. 3 443 465
    • (1993) SIAM J. Optim. , vol.3 , pp. 443-465
    • Pang, J.-S.1    Qi, L.2
  • 30
    • 0001070251 scopus 로고    scopus 로고
    • Equivalence of variational inequality problems to unconstrained optimization
    • J.-M. Peng 1997 Equivalence of variational inequality problems to unconstrained optimization Math. Program. 78 347 356
    • (1997) Math. Program. , vol.78 , pp. 347-356
    • Peng, J.-M.1
  • 31
    • 0000607524 scopus 로고
    • Convergence analysis of some algorithms for solving nonsmooth equations
    • L. Qi 1993 Convergence analysis of some algorithms for solving nonsmooth equations Math. Oper. Res. 18 227 244
    • (1993) Math. Oper. Res. , vol.18 , pp. 227-244
    • Qi, L.1
  • 33
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein choice of the steplength for the gradient method
    • M. Raydan 1993 On the Barzilai and Borwein choice of the steplength for the gradient method IMA J. Numer. Anal. 13 321 326
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 34
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • M. Raydan 1997 The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem SIAM J. Optim. 7 26 33
    • (1997) SIAM J. Optim. , vol.7 , pp. 26-33
    • Raydan, M.1
  • 35
    • 0018922522 scopus 로고
    • Existence and uniqueness of equilibrium points for concave N-person games
    • J.B. Rosen 1965 Existence and uniqueness of equilibrium points for concave N-person games Econometrica 33 520 534
    • (1965) Econometrica , vol.33 , pp. 520-534
    • Rosen, J.B.1
  • 36
    • 0028447256 scopus 로고
    • On relaxation algorithms in computation of noncooperative equilibria
    • S. Uryasev R.Y. Rubinstein 1994 On relaxation algorithms in computation of noncooperative equilibria IEEE Trans. Autom. Control 39 1263 1267
    • (1994) IEEE Trans. Autom. Control , vol.39 , pp. 1263-1267
    • Uryasev, S.1    Rubinstein, R.Y.2
  • 37
    • 0031530152 scopus 로고    scopus 로고
    • Unconstrained optimization reformulations of variational inequality problems
    • N. Yamashita K. Taji M. Fukushima 1997 Unconstrained optimization reformulations of variational inequality problems J. Optim. Theory Appl. 92 439 456
    • (1997) J. Optim. Theory Appl. , vol.92 , pp. 439-456
    • Yamashita, N.1    Taji, K.2    Fukushima, M.3


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