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Volumn 227, Issue 1, 2013, Pages 1-11

Existence and solution methods for equilibria

Author keywords

Auxiliary principle; Coercivity; Equilibrium problem; Monotonicity; Regularization

Indexed keywords

ALGORITHMIC LANGUAGES; COERCIVE FORCE; VARIATIONAL TECHNIQUES;

EID: 84872900380     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2012.11.037     Document Type: Article
Times cited : (166)

References (111)
  • 1
    • 43049166959 scopus 로고    scopus 로고
    • Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory
    • S. Al-Homidan, Q.H. Ansari, and J.C. Yao Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory Nonlinear Analysis: Theory, Methods and Applications 69 2008 126 139
    • (2008) Nonlinear Analysis: Theory, Methods and Applications , vol.69 , pp. 126-139
    • Al-Homidan, S.1    Ansari, Q.H.2    Yao, J.C.3
  • 3
    • 3142557595 scopus 로고    scopus 로고
    • Equilibrium, games, and pricing in transportation and telecommunication networks
    • E. Altman, and L. Wynter Equilibrium, games, and pricing in transportation and telecommunication networks Networks and Spatial Economics 4 2004 7 21
    • (2004) Networks and Spatial Economics , vol.4 , pp. 7-21
    • Altman, E.1    Wynter, L.2
  • 4
    • 79955482712 scopus 로고    scopus 로고
    • A logarithmic quadratic regularization method for solving pseudomonotone equilibrium problems
    • P.N. Anh A logarithmic quadratic regularization method for solving pseudomonotone equilibrium problems Acta Mathematica Vietnamica 34 2009 183 200
    • (2009) Acta Mathematica Vietnamica , vol.34 , pp. 183-200
    • Anh, P.N.1
  • 5
    • 79955468712 scopus 로고    scopus 로고
    • Outer approximation algorithms for pseudomonotone equilibrium problems
    • P.N. Anh, and J.K. Kim Outer approximation algorithms for pseudomonotone equilibrium problems Computers and Mathematics with Applications 61 2011 2588 2595
    • (2011) Computers and Mathematics with Applications , vol.61 , pp. 2588-2595
    • Anh, P.N.1    Kim, J.K.2
  • 7
    • 84928519059 scopus 로고
    • Inverse optimization problems and methods for their solution, in system modelling and optimization
    • A.S. Antipin Inverse optimization problems and methods for their solution, in system modelling and optimization Lecture Notes in Control and Information Sciences 143 1990 544 553
    • (1990) Lecture Notes in Control and Information Sciences , vol.143 , pp. 544-553
    • Antipin, A.S.1
  • 8
    • 0002626282 scopus 로고
    • The convergence of proximal methods to fixed points of extremal mappings and estimates of their rates of convergence
    • A.S. Antipin The convergence of proximal methods to fixed points of extremal mappings and estimates of their rates of convergence Computational Mathematics and Mathematical Physics 35 1995 539 551
    • (1995) Computational Mathematics and Mathematical Physics , vol.35 , pp. 539-551
    • Antipin, A.S.1
  • 11
    • 84890482773 scopus 로고    scopus 로고
    • Generalized Nash Equilibria for the Service Provisioning Problem in Cloud Systems
    • doi:10.1109/TSC.2012.14 in press
    • D. Ardagna, B. Panicucci, M. Passacantando, Generalized Nash Equilibria for the Service Provisioning Problem in Cloud Systems, IEEE Transactions on Services Computing, in press, http://dx.doi.org/10.1109/TSC.2012.14.
    • IEEE Transactions on Services Computing
    • Ardagna, D.1    Panicucci, B.2    Passacantando, M.3
  • 12
    • 0001436273 scopus 로고
    • Existence of an equilibrium for a competitive economy
    • K.J. Arrow, and G. Debreu Existence of an equilibrium for a competitive economy Econometrica 22 1954 265 290
    • (1954) Econometrica , vol.22 , pp. 265-290
    • Arrow, K.J.1    Debreu, G.2
  • 14
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • H.H. Bauschke, and J.M. Borwein On projection algorithms for solving convex feasibility problems SIAM Review 38 1996 367 426
    • (1996) SIAM Review , vol.38 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 15
    • 20044390432 scopus 로고    scopus 로고
    • Numerical solution of saddle point problems
    • M. Benzi, G.H. Golub, and J. Liesen Numerical solution of saddle point problems Acta Numerica 14 2005 1 137
    • (2005) Acta Numerica , vol.14 , pp. 1-137
    • Benzi, M.1    Golub, G.H.2    Liesen, J.3
  • 16
    • 9744264031 scopus 로고    scopus 로고
    • Minimal coercivity conditions for variational inequalities: Application to exceptional families of element
    • M. Bianchi, M. Hadjisavvas, and S. Schaible Minimal coercivity conditions for variational inequalities: application to exceptional families of element Journal of Optimization Theory and Applications 122 2004 1 17
    • (2004) Journal of Optimization Theory and Applications , vol.122 , pp. 1-17
    • Bianchi, M.1    Hadjisavvas, M.2    Schaible, S.3
  • 22
    • 84868374101 scopus 로고    scopus 로고
    • Gap functions and penalization for solving equilibrium problems with nonlinear constraints
    • G. Bigi, and M. Passacantando Gap functions and penalization for solving equilibrium problems with nonlinear constraints Computational Optimization and Applications 53 2012 323 346
    • (2012) Computational Optimization and Applications , vol.53 , pp. 323-346
    • Bigi, G.1    Passacantando, M.2
  • 24
    • 0000034358 scopus 로고
    • From optimization and variational inequalities to equilibrium problems
    • E. Blum, and W. Oettli From optimization and variational inequalities to equilibrium problems The Mathematics Student 63 1994 123 145
    • (1994) The Mathematics Student , vol.63 , pp. 123-145
    • Blum, E.1    Oettli, W.2
  • 29
    • 0000433247 scopus 로고
    • Convergence analysis of a proximal-like minimization algorithm using Bregman functions
    • G. Chen, and M. Teboulle Convergence analysis of a proximal-like minimization algorithm using Bregman functions SIAM Journal of Optimization 3 1993 538 543
    • (1993) SIAM Journal of Optimization , vol.3 , pp. 538-543
    • Chen, G.1    Teboulle, M.2
  • 32
    • 0002036820 scopus 로고
    • Traffic equilibrium and variational inequalities
    • S. Dafermos Traffic equilibrium and variational inequalities Transportation Science 14 1980 42 54
    • (1980) Transportation Science , vol.14 , pp. 42-54
    • Dafermos, S.1
  • 37
    • 33646842320 scopus 로고
    • A generalization of Tychonoff's fixed point theorem
    • K. Fan A generalization of Tychonoff's fixed point theorem Mathematische Annalen 142 1961 305 310
    • (1961) Mathematische Annalen , vol.142 , pp. 305-310
    • Fan, K.1
  • 38
    • 0001667407 scopus 로고
    • A minimax inequality and applications
    • O. Shisha, Academic Press New York
    • K. Fan A minimax inequality and applications O. Shisha, Inequalities Vol. III 1972 Academic Press New York 103 113
    • (1972) Inequalities , vol.3 , pp. 103-113
    • Fan, K.1
  • 39
    • 0031352141 scopus 로고    scopus 로고
    • Engineering and economic applications of complementarity problems
    • M.C. Ferris, and J.-S. Pang Engineering and economic applications of complementarity problems SIAM Review 39 1997 669 713
    • (1997) SIAM Review , vol.39 , pp. 669-713
    • Ferris, M.C.1    Pang, J.-S.2
  • 40
    • 0039325157 scopus 로고    scopus 로고
    • Equilibrium programming using proximal-like algorithms
    • S.D. Flam, and A.S. Antipin Equilibrium programming using proximal-like algorithms Mathematical Programming 78 1997 29 41
    • (1997) Mathematical Programming , vol.78 , pp. 29-41
    • Flam, S.D.1    Antipin, A.S.2
  • 41
    • 0035238863 scopus 로고    scopus 로고
    • Existence theorems for generalized noncoercive equilibrium problems: The quasi-convex case
    • F. Flores-Bazan Existence theorems for generalized noncoercive equilibrium problems: the quasi-convex case SIAM Journal on Optimization 11 2000 675 690
    • (2000) SIAM Journal on Optimization , vol.11 , pp. 675-690
    • Flores-Bazan, F.1
  • 43
    • 0001849165 scopus 로고    scopus 로고
    • On Minty variational principle
    • F. Giannessi, S. Komlósi, T. Rapcsák, Kluwer Academic Publishers
    • F. Giannessi On Minty variational principle F. Giannessi, S. Komlósi, T. Rapcsák, New Trends in Mathematical Programming 1998 Kluwer Academic Publishers 93 99
    • (1998) New Trends in Mathematical Programming , pp. 93-99
    • Giannessi, F.1
  • 44
    • 0348075406 scopus 로고
    • On the penalty method for constrained variational inequalities
    • J.-B. Hiriart-Urruty, W. Oettli, J. Stoer, Lecture Notes in Pure and Applied Mathematics Dekker, New York
    • J. Gwinner On the penalty method for constrained variational inequalities J.-B. Hiriart-Urruty, W. Oettli, J. Stoer, Optimization: Theory and Algorithms vol. 86 1983 Lecture Notes in Pure and Applied Mathematics Dekker, New York 197 211
    • (1983) Optimization: Theory and Algorithms , vol.86 , pp. 197-211
    • Gwinner, J.1
  • 45
    • 1642336903 scopus 로고    scopus 로고
    • Continuity and maximality properties of pseudomonotone operators
    • N. Hadjisavvas Continuity and maximality properties of pseudomonotone operators Journal of Convex Analysis 10 2003 465 475
    • (2003) Journal of Convex Analysis , vol.10 , pp. 465-475
    • Hadjisavvas, N.1
  • 46
    • 0035340070 scopus 로고    scopus 로고
    • Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets
    • B. Hobbs Linear complementarity models of Nash-Cournot competition in bilateral and POOLCO power markets IEEE Transactions on Power Systems 16 2001 194 202
    • (2001) IEEE Transactions on Power Systems , vol.16 , pp. 194-202
    • Hobbs, B.1
  • 47
    • 45749086115 scopus 로고    scopus 로고
    • On certain conditions for the existence of solutions of equilibrium problems
    • A.N. Iusem, G. Kassay, and W. Sosa On certain conditions for the existence of solutions of equilibrium problems Mathematical Programming 116 2009 259 273
    • (2009) Mathematical Programming , vol.116 , pp. 259-273
    • Iusem, A.N.1    Kassay, G.2    Sosa, W.3
  • 48
    • 37549043183 scopus 로고    scopus 로고
    • Inexact proximal point methods for equilibrium problems in banach spaces
    • A.N. Iusem, and M. Nasri Inexact proximal point methods for equilibrium problems in banach spaces Numerical Functional Analysis and Optimization 28 2007 1279 1308
    • (2007) Numerical Functional Analysis and Optimization , vol.28 , pp. 1279-1308
    • Iusem, A.N.1    Nasri, M.2
  • 49
    • 0042730351 scopus 로고    scopus 로고
    • Iterative algorithms for equilibrium problems
    • A.N. Iusem, and W. Sosa Iterative algorithms for equilibrium problems Optimization 52 2003 301 316
    • (2003) Optimization , vol.52 , pp. 301-316
    • Iusem, A.N.1    Sosa, W.2
  • 50
    • 77958481141 scopus 로고    scopus 로고
    • On the proximal point method for equilibrium problems in Hilbert spaces
    • A.N. Iusem, and W. Sosa On the proximal point method for equilibrium problems in Hilbert spaces Optimization 59 2010 1259 1274
    • (2010) Optimization , vol.59 , pp. 1259-1274
    • Iusem, A.N.1    Sosa, W.2
  • 51
    • 13244281672 scopus 로고    scopus 로고
    • Extended auxiliary problem principle using Bregman distances
    • A. Kaplan, and R. Tichatschke Extended auxiliary problem principle using Bregman distances Optimization 53 2004 603 623
    • (2004) Optimization , vol.53 , pp. 603-623
    • Kaplan, A.1    Tichatschke, R.2
  • 53
    • 33744910585 scopus 로고    scopus 로고
    • Game-theoretic analysis of Internet switching with selfish users
    • X. Deng, Y. Ye, Springer-Verlag Berlin
    • A. Kesselman, S. Leonardi, and V. Bonifaci Game-theoretic analysis of Internet switching with selfish users X. Deng, Y. Ye, Internet and Network Economics 2005 Springer-Verlag Berlin 236 245
    • (2005) Internet and Network Economics , pp. 236-245
    • Kesselman, A.1    Leonardi, S.2    Bonifaci, V.3
  • 55
    • 0040186058 scopus 로고    scopus 로고
    • Combined relaxation method for monotone equilibrium problems
    • I.V. Konnov Combined relaxation method for monotone equilibrium problems Journal of Optimization Theory and Applications 111 2001 327 340
    • (2001) Journal of Optimization Theory and Applications , vol.111 , pp. 327-340
    • Konnov, I.V.1
  • 56
    • 0344583837 scopus 로고    scopus 로고
    • Application of the proximal point method to nonmonotone equilibrium problems
    • I.V. Konnov Application of the proximal point method to nonmonotone equilibrium problems Journal of Optimization Theory and Applications 119 2003 317 333
    • (2003) Journal of Optimization Theory and Applications , vol.119 , pp. 317-333
    • Konnov, I.V.1
  • 57
    • 42449101680 scopus 로고    scopus 로고
    • Partial regularization method for equilibrium problems
    • I.V. Konnov Partial regularization method for equilibrium problems Journal of Nonlinear and Convex Analysis 6 2005 497 503
    • (2005) Journal of Nonlinear and Convex Analysis , vol.6 , pp. 497-503
    • Konnov, I.V.1
  • 58
    • 30944453919 scopus 로고    scopus 로고
    • Partial proximal point method for nonmonotone equilibrium problems
    • I.V. Konnov Partial proximal point method for nonmonotone equilibrium problems Optimization Methods and Software 21 2006 373 384
    • (2006) Optimization Methods and Software , vol.21 , pp. 373-384
    • Konnov, I.V.1
  • 60
    • 35148850018 scopus 로고    scopus 로고
    • On variational inequalities for auction market problems
    • I.V. Konnov On variational inequalities for auction market problems Optimization Letters 1 2007 155 162
    • (2007) Optimization Letters , vol.1 , pp. 155-162
    • Konnov, I.V.1
  • 61
    • 84872923602 scopus 로고    scopus 로고
    • Variational inequalities for modeling auction markets with price mappings
    • I.V. Konnov Variational inequalities for modeling auction markets with price mappings Open Operational Research Journal 2 2008 29 37
    • (2008) Open Operational Research Journal , vol.2 , pp. 29-37
    • Konnov, I.V.1
  • 62
    • 79960941550 scopus 로고    scopus 로고
    • Spatial equilibrium problems for auction-type systems
    • I.V. Konnov Spatial equilibrium problems for auction-type systems Russian Mathematics 52 2008 30 44
    • (2008) Russian Mathematics , vol.52 , pp. 30-44
    • Konnov, I.V.1
  • 63
    • 77952090499 scopus 로고    scopus 로고
    • Regularization method for nonmonotone equilibrium problems
    • I.V. Konnov Regularization method for nonmonotone equilibrium problems Journal of Nonlinear and Convex Analysis 10 2009 93 101
    • (2009) Journal of Nonlinear and Convex Analysis , vol.10 , pp. 93-101
    • Konnov, I.V.1
  • 65
    • 79956155400 scopus 로고    scopus 로고
    • Nonmonotone equilibrium problems: Coercivity conditions and weak regularization
    • I.V. Konnov, and D.A. Dyabilkin Nonmonotone equilibrium problems: coercivity conditions and weak regularization Journal of Global Optimization 49 2011 575 587
    • (2011) Journal of Global Optimization , vol.49 , pp. 575-587
    • Konnov, I.V.1    Dyabilkin, D.A.2
  • 66
    • 84872952585 scopus 로고    scopus 로고
    • Descent method with respect to the gap function for nonsmooth equilibrium problems
    • I.V. Konnov, and O.V. Pinyagina Descent method with respect to the gap function for nonsmooth equilibrium problems Russian Mathematics 47 2003 67 73
    • (2003) Russian Mathematics , vol.47 , pp. 67-73
    • Konnov, I.V.1    Pinyagina, O.V.2
  • 68
    • 4243123037 scopus 로고    scopus 로고
    • D-gap functions and descent methods for a class of monotone equilibrium problems
    • I.V. Konnov, and O.V. Pinyagina D-gap functions and descent methods for a class of monotone equilibrium problems Lobachevskii Journal of Mathematics 13 2003 57 65
    • (2003) Lobachevskii Journal of Mathematics , vol.13 , pp. 57-65
    • Konnov, I.V.1    Pinyagina, O.V.2
  • 71
    • 0034406492 scopus 로고    scopus 로고
    • Relaxation algorithms to find Nash equilibria with economic applications
    • J.B. Krawczyk, and S. Uryasev Relaxation algorithms to find Nash equilibria with economic applications Environmental Modeling and Assessment 5 2000 63 73
    • (2000) Environmental Modeling and Assessment , vol.5 , pp. 63-73
    • Krawczyk, J.B.1    Uryasev, S.2
  • 72
    • 48849091648 scopus 로고    scopus 로고
    • On maximal element theorems, variant of Ekeland's variational and their applications
    • L.-J. Lin, and W.-S. Du On maximal element theorems, variant of Ekeland's variational and their applications Nonlinear Analysis: Theory, Methods and Applications 68 2008 1246 1262
    • (2008) Nonlinear Analysis: Theory, Methods and Applications , vol.68 , pp. 1246-1262
    • Lin, L.-J.1    Du, W.-S.2
  • 73
    • 34250007734 scopus 로고    scopus 로고
    • Financial networks with intermediation and transportation network equilibria: A supernetwork equivalence and reinterpretation of the equilibrium conditions with computations
    • Z. Liu, and A. Nagurney Financial networks with intermediation and transportation network equilibria: a supernetwork equivalence and reinterpretation of the equilibrium conditions with computations Computational Management Science 4 2007 243 281
    • (2007) Computational Management Science , vol.4 , pp. 243-281
    • Liu, Z.1    Nagurney, A.2
  • 74
    • 77956933034 scopus 로고    scopus 로고
    • Strong convergence of an inexact proximal point algorithm for equilibrium problems in Banach spaces
    • J. Mashreghia, and M. Nasri Strong convergence of an inexact proximal point algorithm for equilibrium problems in Banach spaces Numerical Functional Analysis and Optimization 31 2010 1053 1071
    • (2010) Numerical Functional Analysis and Optimization , vol.31 , pp. 1053-1071
    • Mashreghia, J.1    Nasri, M.2
  • 75
    • 15844387395 scopus 로고    scopus 로고
    • On auxiliary principle for equilibrium problems
    • P. Daniele, F. Giannessi, A. Maugeri, Kluwer Academic Publishers Norwell
    • G. Mastroeni On auxiliary principle for equilibrium problems P. Daniele, F. Giannessi, A. Maugeri, Equilibrium Problems and Variational Models 2003 Kluwer Academic Publishers Norwell 289 298
    • (2003) Equilibrium Problems and Variational Models , pp. 289-298
    • Mastroeni, G.1
  • 76
    • 0242653626 scopus 로고    scopus 로고
    • Gap functions for equilibrium problems
    • G. Mastroeni Gap functions for equilibrium problems Journal of Global Optimization 27 2003 411 426
    • (2003) Journal of Global Optimization , vol.27 , pp. 411-426
    • Mastroeni, G.1
  • 77
    • 43049083737 scopus 로고    scopus 로고
    • Risk-adjusted probability measures in portfolio optimization with coherent measures of risk
    • N. Miller, and A. Ruszczynski Risk-adjusted probability measures in portfolio optimization with coherent measures of risk European Journal of Operational Research 191 2008 193 206
    • (2008) European Journal of Operational Research , vol.191 , pp. 193-206
    • Miller, N.1    Ruszczynski, A.2
  • 78
    • 0042884758 scopus 로고
    • On the generalization of a direct method of the calculus of variations
    • G.J. Minty On the generalization of a direct method of the calculus of variations Bulletin American Mathematical Society 73 1967 315 321
    • (1967) Bulletin American Mathematical Society , vol.73 , pp. 315-321
    • Minty, G.J.1
  • 79
    • 34547367379 scopus 로고    scopus 로고
    • Equilibrium problems with complementarity constraints: Case study with applications to oligopolistic markets
    • B.S. Mordukhovich, J.V. Outrata, and M. Cervinka Equilibrium problems with complementarity constraints: case study with applications to oligopolistic markets Optimization 56 2007 479 494
    • (2007) Optimization , vol.56 , pp. 479-494
    • Mordukhovich, B.S.1    Outrata, J.V.2    Cervinka, M.3
  • 80
    • 0242648275 scopus 로고    scopus 로고
    • Proximal point methods extended to equilibrium problems
    • A. Moudafi Proximal point methods extended to equilibrium problems Journal of Natural Geometry 15 1999 91 100
    • (1999) Journal of Natural Geometry , vol.15 , pp. 91-100
    • Moudafi, A.1
  • 81
    • 4844224680 scopus 로고    scopus 로고
    • Second-order differential proximal methods for equilibrium problems
    • (Article No. 18)
    • A. Moudafi Second-order differential proximal methods for equilibrium problems Journal of Inequalities in Pure and Applied Mathematics 4 2003 (Article No. 18)
    • (2003) Journal of Inequalities in Pure and Applied Mathematics , vol.4
    • Moudafi, A.1
  • 82
    • 37549015238 scopus 로고    scopus 로고
    • On finite and strong convergence of a proximal method for equilibrium problems
    • A. Moudafi On finite and strong convergence of a proximal method for equilibrium problems Numerical Functional Analysis and Optimization 28 2007 1347 1354
    • (2007) Numerical Functional Analysis and Optimization , vol.28 , pp. 1347-1354
    • Moudafi, A.1
  • 83
    • 13244283821 scopus 로고    scopus 로고
    • Proximal and dynamical approaches to equilibrium problems
    • M. Théra, R. Tichatschke, Springer Berlin
    • A. Moudafi, and M. Théra Proximal and dynamical approaches to equilibrium problems M. Théra, R. Tichatschke, Ill-Posed Variational Problems and Regularization Techniques 1999 Springer Berlin 187 201
    • (1999) Ill-Posed Variational Problems and Regularization Techniques , pp. 187-201
    • Moudafi, A.1    Théra, M.2
  • 84
    • 70349656477 scopus 로고    scopus 로고
    • Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model
    • L.D. Muu, and T.D. Quoc Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model Journal of Optimization Theory and Applications 142 2009 185 204
    • (2009) Journal of Optimization Theory and Applications , vol.142 , pp. 185-204
    • Muu, L.D.1    Quoc, T.D.2
  • 86
    • 77956439553 scopus 로고    scopus 로고
    • Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: A supply chain network perspective
    • A. Nagurney Formulation and analysis of horizontal mergers among oligopolistic firms with insights into the merger paradox: a supply chain network perspective Computational Management Science 7 2010 377 406
    • (2010) Computational Management Science , vol.7 , pp. 377-406
    • Nagurney, A.1
  • 87
    • 32544434072 scopus 로고    scopus 로고
    • International financial networks with intermediation: Modeling, analysis, and computations
    • A. Nagurney, and J. Cruz International financial networks with intermediation: modeling, analysis, and computations Computational Management Science 1 2003 31 58
    • (2003) Computational Management Science , vol.1 , pp. 31-58
    • Nagurney, A.1    Cruz, J.2
  • 88
    • 32544453700 scopus 로고    scopus 로고
    • Financial networks with intermediation: Risk management with variable weights
    • A. Nagurney, and K. Ke Financial networks with intermediation: risk management with variable weights European Journal of Operational Research 172 2006 40 63
    • (2006) European Journal of Operational Research , vol.172 , pp. 40-63
    • Nagurney, A.1    Ke, K.2
  • 90
    • 0001730497 scopus 로고
    • Non-cooperative games
    • J.F. Nash Non-cooperative games Annals of Mathematics 54 1951 286 295
    • (1951) Annals of Mathematics , vol.54 , pp. 286-295
    • Nash, J.F.1
  • 92
    • 67349087936 scopus 로고    scopus 로고
    • The interior proximal extragradient method for solving equilibrium problems
    • T.T.V. Nguyen, J.J. Strodiot, and V.H. Nguyen The interior proximal extragradient method for solving equilibrium problems Journal of Global Optimization 44 2009 175 192
    • (2009) Journal of Global Optimization , vol.44 , pp. 175-192
    • Nguyen, T.T.V.1    Strodiot, J.J.2    Nguyen, V.H.3
  • 94
    • 77952557725 scopus 로고    scopus 로고
    • Design of cognitive radio systems under temperature-interference constraints: A variational inequality approach
    • J.-S. Pang, G. Scutari, D.P. Palomar, and F. Facchinei Design of cognitive radio systems under temperature-interference constraints: a variational inequality approach IEEE Transactions on Signal Processing 58 2010 3251 3271
    • (2010) IEEE Transactions on Signal Processing , vol.58 , pp. 3251-3271
    • Pang, J.-S.1    Scutari, G.2    Palomar, D.P.3    Facchinei, F.4
  • 96
    • 84855418978 scopus 로고    scopus 로고
    • Dual extragradient algorithms extended to equilibrium problems
    • T.D. Quoc, P.N. Anh, and L.D. Muu Dual extragradient algorithms extended to equilibrium problems Journal of Global Optimization 52 2012 139 159
    • (2012) Journal of Global Optimization , vol.52 , pp. 139-159
    • Quoc, T.D.1    Anh, P.N.2    Muu, L.D.3
  • 97
    • 55849087997 scopus 로고    scopus 로고
    • Extragradient algorithms extended to equilibrium problems
    • T.D. Quoc, M.L. Dung, and V.H. Nguyen Extragradient algorithms extended to equilibrium problems Optimization 57 2008 749 776
    • (2008) Optimization , vol.57 , pp. 749-776
    • Quoc, T.D.1    Dung, M.L.2    Nguyen, V.H.3
  • 98
    • 84862011673 scopus 로고    scopus 로고
    • Iterative methods for solving monotone equilibrium problems via dual gap functions
    • T.D. Quoc, and L.D. Muu Iterative methods for solving monotone equilibrium problems via dual gap functions Computational Optimization and Applications 51 2012 709 728
    • (2012) Computational Optimization and Applications , vol.51 , pp. 709-728
    • Quoc, T.D.1    Muu, L.D.2
  • 99
    • 33746253909 scopus 로고    scopus 로고
    • An analytic center cutting plane algorithm for finding equilibrium points
    • F.M.P. Raupp, and W. Sosa An analytic center cutting plane algorithm for finding equilibrium points RAIRO Operations Research 40 2006 37 52
    • (2006) RAIRO Operations Research , vol.40 , pp. 37-52
    • Raupp, F.M.P.1    Sosa, W.2
  • 101
    • 84858171757 scopus 로고    scopus 로고
    • A relaxed projection method for finite-dimensional equilibrium problems
    • S. Scheimberg, and P.S.M. Santos A relaxed projection method for finite-dimensional equilibrium problems Optimization 60 2011 1193 1208
    • (2011) Optimization , vol.60 , pp. 1193-1208
    • Scheimberg, S.1    Santos, P.S.M.2
  • 102
    • 74949134488 scopus 로고    scopus 로고
    • Competitive optimization of cognitive radio MIMO systems via game theory
    • D.P. Palomar, Y.C. Eldar, Cambridge University Press Cambridge
    • G. Scutari, D.P. Palomar, and S. Barbarossa Competitive optimization of cognitive radio MIMO systems via game theory D.P. Palomar, Y.C. Eldar, Convex Optimization in Signal Processing and Communications 2010 Cambridge University Press Cambridge 387 442
    • (2010) Convex Optimization in Signal Processing and Communications , pp. 387-442
    • Scutari, G.1    Palomar, D.P.2    Barbarossa, S.3
  • 104
    • 0346899423 scopus 로고    scopus 로고
    • Merit functions and error bounds for generalized variational inequalities
    • M.V. Solodov Merit functions and error bounds for generalized variational inequalities Journal of Mathematical Analysis and Applications 287 2003 405 414
    • (2003) Journal of Mathematical Analysis and Applications , vol.287 , pp. 405-414
    • Solodov, M.V.1
  • 106
    • 33845619015 scopus 로고    scopus 로고
    • Modified combined relaxation method for general monotone equilibrium problems in Hilbert spaces
    • L.C. Zeng, and J.C. Yao Modified combined relaxation method for general monotone equilibrium problems in Hilbert spaces Journal of Optimization Theory and Applications 131 2006 469 483
    • (2006) Journal of Optimization Theory and Applications , vol.131 , pp. 469-483
    • Zeng, L.C.1    Yao, J.C.2
  • 107
    • 63849292451 scopus 로고    scopus 로고
    • Unconstrained optimization reformulations of equilibrium problems
    • L. Zhang, and J.Y. Han Unconstrained optimization reformulations of equilibrium problems Acta Mathematica Sinica 25 2009 343 354
    • (2009) Acta Mathematica Sinica , vol.25 , pp. 343-354
    • Zhang, L.1    Han, J.Y.2
  • 108
    • 67349199161 scopus 로고    scopus 로고
    • An algorithm based on the generalized D-gap function for equilibrium problems
    • L. Zhang, and S.-Y. Wu An algorithm based on the generalized D-gap function for equilibrium problems Journal of Computational and Applied Mathematics 231 2009 403 411
    • (2009) Journal of Computational and Applied Mathematics , vol.231 , pp. 403-411
    • Zhang, L.1    Wu, S.-Y.2
  • 109
    • 77952470349 scopus 로고    scopus 로고
    • Convergence and error bound of a D-gap function based Newton-type algorithm for equilibrium problems
    • L. Zhang, S.-Y. Wu, and S.-C. Fang Convergence and error bound of a D-gap function based Newton-type algorithm for equilibrium problems Journal of Industrial and Management Optimization 6 2010 333 346
    • (2010) Journal of Industrial and Management Optimization , vol.6 , pp. 333-346
    • Zhang, L.1    Wu, S.-Y.2    Fang, S.-C.3
  • 110
    • 0033244578 scopus 로고    scopus 로고
    • Exceptional families and existence theorems for variational inequalities problems
    • Y.B. Zhao, J.Y. Han, and H.D. Qi Exceptional families and existence theorems for variational inequalities problems Journal of Optimization Theory and Applications 101 1999 475 495
    • (1999) Journal of Optimization Theory and Applications , vol.101 , pp. 475-495
    • Zhao, Y.B.1    Han, J.Y.2    Qi, H.D.3
  • 111
    • 36048936264 scopus 로고    scopus 로고
    • A network equilibrium framework for internet advertising: Models, qualitative analysis, and algorithms
    • L. Zhao, and A. Nagurney A network equilibrium framework for internet advertising: models, qualitative analysis, and algorithms European Journal of Operational Research 187 2008 456 472
    • (2008) European Journal of Operational Research , vol.187 , pp. 456-472
    • Zhao, L.1    Nagurney, A.2


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