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Volumn 53, Issue 2, 2012, Pages 323-346

Gap functions and penalization for solving equilibrium problems with nonlinear constraints

Author keywords

Descent direction; Equilibrium problems; Exact penalization; Gap function

Indexed keywords

COMPETITION; GLOBAL OPTIMIZATION; OPTIMIZATION;

EID: 84868374101     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-012-9481-z     Document Type: Article
Times cited : (20)

References (25)
  • 2
    • 0000034358 scopus 로고
    • From optimization and variational inequalities to equilibrium problems
    • Blum, E., Oettli, W.: From optimization and variational inequalities to equilibrium problems. Math. Stud. 63, 123-145 (1994)
    • (1994) Math. Stud. , vol.63 , pp. 123-145
    • Blum, E.1    Oettli, W.2
  • 3
    • 80052405985 scopus 로고
    • U.S. Dept. of Commerce, Urban Planning Division, Washington, DC
    • Bureau of Public Roads: Traffic Assignment Manual. U.S. Dept. of Commerce, Urban Planning Division, Washington, DC (1964)
    • (1964) Bureau of Public Roads: Traffic Assignment Manual
  • 4
    • 10644265114 scopus 로고    scopus 로고
    • Descent methods for equilibrium problems in a Banach space
    • Chadli, O., Konnov, I.V., Yao, J.C.: Descent methods for equilibrium problems in a Banach space. Comput. Math. Appl. 48, 609-616 (2004)
    • (2004) Comput. Math. Appl. , vol.48 , pp. 609-616
    • Chadli, O.1    Konnov, I.V.2    Yao, J.C.3
  • 7
    • 3043003867 scopus 로고
    • Exact penalty functions for nondifferentiable programming problems
    • Plenum, New York
    • Di Pillo, G., Facchinei, F.: Exact penalty functions for nondifferentiable programming problems. In: Nonsmooth Optimization and Related Topics, pp. 89-107. Plenum, New York (1989)
    • (1989) Nonsmooth Optimization and Related Topics , pp. 89-107
    • Di Pillo, G.1    Facchinei, F.2
  • 8
    • 34848903352 scopus 로고    scopus 로고
    • Generalized Nash equilibrium problems
    • Facchinei, F., Kanzow, C.: Generalized Nash equilibrium problems. 4OR 5, 173-210 (2007)
    • (2007) 4OR , vol.5 , pp. 173-210
    • Facchinei, F.1    Kanzow, C.2
  • 10
    • 0001667407 scopus 로고
    • A minimax inequality and applications
    • Academic Press, New York
    • Fan, K.: A minimax inequality and applications. In: Inequalities, III, pp. 103-113. Academic Press, New York (1972)
    • (1972) Inequalities , vol.3 , pp. 103-113
    • Fan, K.1
  • 11
    • 0026763569 scopus 로고
    • Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
    • Fukushima, M.: Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems. Math. Program. 53, 99-110 (1992)
    • (1992) Math. Program. , vol.53 , pp. 99-110
    • Fukushima, M.1
  • 12
    • 0015571360 scopus 로고
    • Directional derivatives for extremal-value functions with applications to the completely convex case
    • Hogan, W.: Directional derivatives for extremal-value functions with applications to the completely convex case. Oper. Res. 21, 188-209 (1973)
    • (1973) Oper. Res. , vol.21 , pp. 188-209
    • Hogan, W.1
  • 13
    • 0001683067 scopus 로고
    • Point-to-set maps in Mathematical Programming
    • Hogan, W.: Point-to-set maps in Mathematical Programming. SIAM Rev. 15, 591-603 (1973)
    • (1973) SIAM Rev , vol.15 , pp. 591-603
    • Hogan, W.1
  • 15
    • 28244473665 scopus 로고    scopus 로고
    • Descent methods for monotone equilibrium problems in Banach spaces
    • DOI 10.1016/j.cam.2005.04.004, PII S037704270500213X
    • Konnov, I.V., Ali, M.S.S.: Descent methods for monotone equilibrium problems in Banach spaces. J. Comput. Appl. Math. 188, 165-179 (2006) (Pubitemid 41705815)
    • (2006) Journal of Computational and Applied Mathematics , vol.188 , Issue.2 , pp. 165-179
    • Konnov, I.V.1    Ali, M.S.S.2
  • 16
    • 85016662742 scopus 로고    scopus 로고
    • D-gap functions for a class of equilibrium problems in Banach spaces
    • Konnov, I.V., Pinyagina, O.V.: D-gap functions for a class of equilibrium problems in Banach spaces. Comput. Methods Appl. Math. 3, 274-286 (2003)
    • (2003) Comput. Methods Appl. Math. , vol.3 , pp. 274-286
    • Konnov, I.V.1    Pinyagina, O.V.2
  • 17
    • 0023456178 scopus 로고
    • Algorithms for the network oligopoly problem
    • Marcotte, P.: Algorithms for the network oligopoly problem. J. Oper. Res. Soc. 38, 1051-1065 (1987)
    • (1987) J. Oper. Res. Soc. , vol.38 , pp. 1051-1065
    • Marcotte, P.1
  • 18
    • 0242653626 scopus 로고    scopus 로고
    • Gap functions for equilibrium problems
    • Mastroeni, G.: Gap functions for equilibrium problems. J. Glob. Optim. 27, 411-426 (2003)
    • (2003) J. Glob. Optim. , vol.27 , pp. 411-426
    • Mastroeni, G.1
  • 19
    • 0020178616 scopus 로고
    • A mathematical programming approach for determining oligopolistic market equilibrium
    • Murphy, F.H., Sherali, H.D., Soyster, A.L.: A mathematical programming approach for determining oligopolistic market equilibrium. Math. Program. 24, 92-106 (1982)
    • (1982) Math. Program. , vol.24 , pp. 92-106
    • Murphy, F.H.1    Sherali, H.D.2    Soyster, A.L.3
  • 20
    • 0000579136 scopus 로고
    • Existence and uniqueness of equilibrium points for concave n-games
    • Rosen, J.B.: Existence and uniqueness of equilibrium points for concave n-games. Econometrica 33, 520-534 (1965)
    • (1965) Econometrica , vol.33 , pp. 520-534
    • Rosen, J.B.1
  • 21
    • 0030303859 scopus 로고    scopus 로고
    • A new merit function and a successive quadratic programming algorithm for variational inequality problems
    • Taji, K., Fukushima, M.: A new merit function and a successive quadratic programming algorithm for variational inequality problems. SIAM J. Optim. 6, 704-713 (1996)
    • (1996) SIAM J. Optim. , vol.6 , pp. 704-713
    • Taji, K.1    Fukushima, M.2
  • 22
    • 67651018689 scopus 로고    scopus 로고
    • Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions
    • von Heusinger, A., Kanzow, C.: Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Comput. Optim. Appl. 43, 353-377 (2009)
    • (2009) Comput. Optim. Appl. , vol.43 , pp. 353-377
    • Von Heusinger, A.1    Kanzow, C.2
  • 23
    • 63849292451 scopus 로고    scopus 로고
    • Unconstrained optimization reformulations of equilibrium problems
    • Zhang, L., Han, J.Y.: Unconstrained optimization reformulations of equilibrium problems. Acta Math. Sin. Engl. Ser. 25, 343-354 (2009)
    • (2009) Acta Math. Sin. Engl. Ser. , vol.25 , pp. 343-354
    • Zhang, L.1    Han, J.Y.2
  • 24
    • 67349199161 scopus 로고    scopus 로고
    • An algorithm based on the generalized D-gap function for equilibrium problems
    • Zhang, L.,Wu, S.-Y.: An algorithm based on the generalized D-gap function for equilibrium problems. J. Comput. Appl. Math. 231, 403-411 (2009)
    • (2009) J. Comput. Appl. Math. , vol.231 , pp. 403-411
    • Zhang, L.1    Wu, S.-Y.2
  • 25
    • 0010759844 scopus 로고
    • Modified descent methods for solving the monotone variational inequality problem
    • Zhu, D.L., Marcotte, P.: Modified descent methods for solving the monotone variational inequality problem. Oper. Res. Lett. 14, 111-120 (1993)
    • (1993) Oper. Res. Lett. , vol.14 , pp. 111-120
    • Zhu, D.L.1    Marcotte, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.