메뉴 건너뛰기




Volumn 52, Issue 2, 2012, Pages 415-437

Smoothing approach to Nash equilibrium formulations for a class of equilibrium problems with shared complementarity constraints

Author keywords

Equilibrium problem with equilibrium constraints; Global Nash equilibrium; Nash equilibrium problem; P matrix linear complementarity problem; Smoothing approximation; Stationary Nash equilibrium

Indexed keywords

COMPLEMENTARITY CONSTRAINT; COMPLEMENTARITY SYSTEMS; EQUILIBRIUM CONSTRAINT; EQUILIBRIUM PROBLEM; LINEAR COMPLEMENTARITY; LINEAR COMPLEMENTARITY PROBLEMS; MATHEMATICAL PROGRAM WITH EQUILIBRIUM CONSTRAINTS; NASH EQUILIBRIA; NON-SMOOTH; NUMERICAL EXAMPLE; P-MATRIX; SMOOTHING APPROXIMATION; SMOOTHING METHODS; SOLUTION CONCEPTS; SPECIAL CLASS; VARIATIONAL INEQUALITIES;

EID: 84861910612     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-011-9416-0     Document Type: Article
Times cited : (9)

References (22)
  • 1
    • 1342303387 scopus 로고    scopus 로고
    • A smoothing method for a mathematical program with P-matrix linear complementarity constraints
    • 2035714 1046.90086 10.1023/B:COAP.0000013057.54647.6d
    • X. Chen M. Fukushima 2004 A smoothing method for a mathematical program with P-matrix linear complementarity constraints Comput. Optim. Appl. 27 223 246 2035714 1046.90086 10.1023/B:COAP.0000013057.54647.6d
    • (2004) Comput. Optim. Appl. , vol.27 , pp. 223-246
    • Chen, X.1    Fukushima, M.2
  • 4
    • 0000425448 scopus 로고    scopus 로고
    • A smoothing method for mathematical programs with equilibrium constraints
    • 1689366 0959.65079 10.1007/s101070050048
    • F. Facchinei H. Jiang L. Qi 1999 A smoothing method for mathematical programs with equilibrium constraints Math. Program. 85 107 134 1689366 0959.65079 10.1007/s101070050048
    • (1999) Math. Program. , vol.85 , pp. 107-134
    • Facchinei, F.1    Jiang, H.2    Qi, L.3
  • 6
    • 84948263182 scopus 로고
    • A special Newton-type optimization method
    • 1247636 0814.65063 10.1080/02331939208843795
    • A. Fischer 1992 A special Newton-type optimization method Optimization 24 269 284 1247636 0814.65063 10.1080/02331939208843795
    • (1992) Optimization , vol.24 , pp. 269-284
    • Fischer, A.1
  • 7
    • 0001787420 scopus 로고    scopus 로고
    • Convergence of a smoothing continuation method for mathematical programs with complementarity constraints
    • M. Théra R. Tichatschke (eds). Springer Berlin. 10.1007/978-3-642-45780-7-7
    • Fukushima, M.; Pang, J.S.: Convergence of a smoothing continuation method for mathematical programs with complementarity constraints. In: Théra, M.; Tichatschke, R. (eds.) Ill-posed Variational Problems and Regularization Techniques. Lect. Notes Econ. Math, vol. 477, pp. 99-110. Springer, Berlin (1999)
    • (1999) Ill-posed Variational Problems and Regularization Techniques Lect. Notes Econ. Math , Issue.477 , pp. 99-110
    • Fukushima, M.1    Pang, J.S.2
  • 8
    • 0032047752 scopus 로고    scopus 로고
    • A globally convergent sequential programming algorithm for mathematical programs with linear complementarity constraints
    • 1609612 0904.90153 10.1023/A:1018359900133
    • M. Fukushima Z.Q. Luo J.S. Pang 1998 A globally convergent sequential programming algorithm for mathematical programs with linear complementarity constraints Comput. Optim. Appl. 10 5 30 1609612 0904.90153 10.1023/A: 1018359900133
    • (1998) Comput. Optim. Appl. , vol.10 , pp. 5-30
    • Fukushima, M.1    Luo, Z.Q.2    Pang, J.S.3
  • 9
    • 46749133536 scopus 로고    scopus 로고
    • Approximations of Nash equilibria
    • 1216.91003 10.1007/s10107-007-0156-y
    • G. Gürkan J.S. Pang 2009 Approximations of Nash equilibria Math. Program.; Ser. B 117 223 253 1216.91003 10.1007/s10107-007-0156-y
    • (2009) Math. Program.; Ser. B , vol.117 , pp. 223-253
    • Gürkan, G.1    Pang, J.S.2
  • 10
    • 0034186850 scopus 로고    scopus 로고
    • Strategic gaming analysis for electric power networks: An MPEC approach
    • 10.1109/59.867153
    • B.F. Hobbs C. Metzler J.S. Pang 2000 Strategic gaming analysis for electric power networks: An MPEC approach IEEE Trans. Power Syst. 15 638 645 10.1109/59.867153
    • (2000) IEEE Trans. Power Syst. , vol.15 , pp. 638-645
    • Hobbs, B.F.1    Metzler, C.2    Pang, J.S.3
  • 11
    • 38549176844 scopus 로고    scopus 로고
    • Using EPECs to model bilevel games in restructured electricity markets with locational prices
    • 2360950 1167.91357 10.1287/opre.1070.0431
    • X. Hu D. Ralph 2007 Using EPECs to model bilevel games in restructured electricity markets with locational prices Oper. Res. 55 809 827 2360950 1167.91357 10.1287/opre.1070.0431
    • (2007) Oper. Res. , vol.55 , pp. 809-827
    • Hu, X.1    Ralph, D.2
  • 12
    • 45749115803 scopus 로고    scopus 로고
    • Variational convergence of bivariate functions: Lopsided convergence
    • 1162.65036 10.1007/s10107-007-0122-8
    • A. Jofré R.J.-B. Wets 2009 Variational convergence of bivariate functions: lopsided convergence Math. Program.; Ser. B 116 275 295 1162.65036 10.1007/s10107-007-0122-8
    • (2009) Math. Program.; Ser. B , vol.116 , pp. 275-295
    • Jofré, A.1    Wets, R.J.-B.2
  • 13
    • 0022667727 scopus 로고
    • Approximation to optimization problems: An elementary review
    • 830103 0592.49010 10.1287/moor.11.1.9
    • P. Kall 1986 Approximation to optimization problems: An elementary review Math. Oper. Res. 11 9 18 830103 0592.49010 10.1287/moor.11.1.9
    • (1986) Math. Oper. Res. , vol.11 , pp. 9-18
    • Kall, P.1
  • 14
    • 0030517292 scopus 로고    scopus 로고
    • Some noninterior continuation methods for linear complementarity problem
    • 1410705 0868.90123 10.1137/S0895479894273134
    • C. Kanzow 1996 Some noninterior continuation methods for linear complementarity problem SIAM J. Matrix Anal. Appl. 17 851 868 1410705 0868.90123 10.1137/S0895479894273134
    • (1996) SIAM J. Matrix Anal. Appl. , vol.17 , pp. 851-868
    • Kanzow, C.1
  • 15
    • 0032131672 scopus 로고    scopus 로고
    • Solving box constrained variational inequalities by using the natural residual with D-gap function globalization
    • 1664233 0941.90070 10.1016/S0167-6377(98)00023-6
    • C. Kanzow M. Fukushima 1998 Solving box constrained variational inequalities by using the natural residual with D-gap function globalization Oper. Res. Lett. 23 45 51 1664233 0941.90070 10.1016/S0167-6377(98)00023-6
    • (1998) Oper. Res. Lett. , vol.23 , pp. 45-51
    • Kanzow, C.1    Fukushima, M.2
  • 17
    • 0002021736 scopus 로고
    • Equilibrium points in n-person games
    • 31701 0036.01104 10.1073/pnas.36.1.48
    • J.F. Nash 1950 Equilibrium points in n-person games Proc. Natl. Acad. Sci. USA 36 48 49 31701 0036.01104 10.1073/pnas.36.1.48
    • (1950) Proc. Natl. Acad. Sci. USA , vol.36 , pp. 48-49
    • Nash, J.F.1
  • 18
    • 0001730497 scopus 로고
    • Non-cooperative games
    • 43432 0045.08202 10.2307/1969529
    • J.F. Nash 1951 Non-cooperative games Ann. Math. 54 286 295 43432 0045.08202 10.2307/1969529
    • (1951) Ann. Math. , vol.54 , pp. 286-295
    • Nash, J.F.1
  • 20
    • 20444502586 scopus 로고    scopus 로고
    • Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
    • 2164953 1115.90059 10.1007/s10287-004-0010-0 Erratum, ibid. 6, 373-375 (2009)
    • J.S. Pang M. Fukushima 2005 Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games Comput. Manag. Sci. 2 21 56 2164953 1115.90059 10.1007/s10287-004-0010-0 Erratum, ibid. 6, 373-375 (2009)
    • (2005) Comput. Manag. Sci. , vol.2 , pp. 21-56
    • Pang, J.S.1    Fukushima, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.