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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 66, 2017 - Issue 7
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Original Articles

A half-space projection method for solving generalized Nash equilibrium problems

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Pages 1119-1134 | Received 20 Nov 2016, Accepted 26 Apr 2017, Published online: 22 May 2017

References

  • Debreu G. A social equilibrium existence theorem. Proc Nat Acad Sci. 1952;38:886–893.
  • Arrow KJ, Debreu G. Existence of an equilibrium for a competitive economy. Econometrica. 1954;22(3):265–290.
  • Robinson SM. Shadow prices for measures of effectiveness. I: linear model. Oper Res. 1993;41:518–535.
  • Robinson SM. Shadow prices for measures of effectiveness. II: general model. Oper Res. 1993;41:536–548.
  • Wei JY, Smeers Y. Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Oper Res. 1999;47:102–112.
  • Hobbs BF, Pang JS. Nash-Cournot equilibrium in electric power markets with piecewise linear demand functions and joint constraints. Oper Res. 2007;55:113–127.
  • Contreras J, Klusch M, Krawczyk J. Numerical solutions to Nash-Cournot equilibria in coupled constraint electricity markets. IEEE Trans Power Syst. 2004;19:195–206.
  • Breton M, Zaccour G, Zahaf M. A game-theoretic formulation of joint implementation of environmental projects. Eur J Oper Res. 2006;168:221–239.
  • Pang JS, Scutari G, Facchinei F, et al. Distributed power allocation with rate constraints in Gaussian parallel interference channels. IEEE Trans Inform Theory. 2007;54:3471–3489.
  • Brückner M, Kanzow C, Scheffer T. Static prediction games for adversarial learning problems. J Mach Learn Res. 2012;13:2617–2654.
  • Dutang C, Albrecher H, Loisel S. Competition among non-life insurers under solvency constraints: a game-theoretic approach. Eur J Oper Res. 2013;231:702–711.
  • Contreras J, Krawczyk J, Zuccollo J, et al. Competition of thermal electricity generators with coupled transmission and emission constraints. J Energy Eng. 2013;139:239–252.
  • Han Z, Niyato D, Saad W. Game theory in wireless and communication networks. New York (NY): Cambridge University Press; 2012.
  • Anselmi J, Ardagna D, Passacantando M. Generalized Nash equilibria for SaaS/PaaS clouds. Eur J Oper Res. 2014;236(1):326–339.
  • Scutari G, Palomar DP, Barbarossa S. Competitive optimization of cognitive radio MIMO systems via game theory. In: Palomar DP, Eldar YC, editors. Convex optimization in signal processing and communications. Cambridge: Cambridge University Press; 2009. p. 387–442.
  • Bensoussan A. Points de Nash dans le cas de fonctionnelles quadratiques et jeux differentiels lineaires a N personnes. SIAM J Control. 1974;12:460–499.
  • Harker PT. Generalized Nash games and quasi-variational inequalities. Eur J Oper. 1991;54:81–94.
  • Kocvara M, Outrata J. On a class of quasi-variational inequalities. Optim Methods Softw. 1995;5:275–295.
  • Bertsekas DP, Tsitsiklis JN. Parallel and distributed computation. Numerical methods. Englewood Cliffs (NJ): Prentice-Hall; 1989.
  • Goldstein AA. Convex programming in Hilbert space. Bull Am Math Soc. 1964;70:709–710.
  • Levitin ES, Polyak BT. Constrained minimization problems. USSR Comput Math Math Phys. 1966;6:1–50.
  • Korpelevich GM. The extragradient method for finding saddle points and other problems. Matecon. 1976;17(10):747–756.
  • Khobotov EN. Modification of the extragradient method for solving variational inequalities and certain optimization problems. USSR Comput Math Math Phys. 1987;27:120–127.
  • Xiu NH, Zhang JZ. Some recent advances in projection-type methods for variational inequalities. J Comput Appl Math. 2003;152:559–585.
  • Solodov MV, Svaiter BF. A new projection method for variational inequality problems. SIAM J Control Optim. 1999;37(3):765–776.
  • Konnov IV. Combined relaxation methods for finding equilibrium points and solving related problems. Russ Math (Iz VUZ). 1993;37(2):44–51.
  • Konnov IV. Combined relaxation methods for generalized monotone variational inequalities. In: Generalized convexity and related topics. Vol. 583, Lecture notes in economics and mathematical systems. Berlin: Springer; 2007.
  • Konnov IV. Combined relaxation methods for variational inequalities. Berlin: Springer-Verlag; 2001.
  • He BS. A class of projection and contraction methods for monotone variational inequalities. Appl Math Optim. 1997;35:69–76.
  • Han DR, Lo HK. Two new self-adaptive projection methods for variational inequality problems. Comput Math Appl. 2002;43:1529–1537.
  • Han DR, Lo HK, Wang ZW. A simple self-adaptive alternating direction method for linear variational inequality problems. Comput Math Appl. 2007;53(10):1595–1604.
  • Yan XH, Han DR, Sun WY. A self-adaptive projection method with improved step-size for solving variational inequalities. Comput Math Appl. 2008;55:819–832.
  • Censor Y, Gibali A, Reich S. Extensions of korpelevichs extragradient method for the variational inequality problem in Euclidean space. Optimization. 2012;61(9):1119–1132.
  • Noor M. Some recent advances in variational inequalities, part I: basic concepts. New Zeal J Math. 1997;26:53–80.
  • Wang YJ, Xiu NH, Wang CY. Unified framework of extragradient-type methods for pseudomonotone variational inequalities. J Optim Theory Appl. 2001;111(3):641–656.
  • Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. New York (NY): Springer-Verlag; 2003.
  • Zhang JZ, Qu B, Xiu NH. Some projection-like methods for the generalized Nash equilibria. Comput Optim Appl. 2010;45:89–109.
  • Han DR, Zhang HC, Qian G, et al. An improved two-step method for solving generalized Nash equilibrium problems. Eur J Oper. 2012;216:613–623.
  • Strodiot JJ, Nguyen TTV, Nguyen VH. A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems. J Glob Optim. 2013;56:373–397.
  • Ye ML. A cutting hyperplane projection method for solving generalized quasi-variational inequalities. J Oper Res Soc China. 2016;4(4):483–501.
  • Zarantonello EH. Projections on convex sets in hilbert space and spectral theory contributions to nonlinear functional analysis. New York (NY): Academic Press; 1971.
  • Gafni EM, Bertsekas DP. Two-metric projection problems and descent methods for asymmetric variational inequality problems. Math Program. 1984;53:99–110.
  • He YR. A new double projection algorithm for variational inequalities. J Comput Appl Math. 2006;185:166–173.
  • Outrata J, Zowe J. A numerical approach to optimization problems with variational inequality constraints. Math Program. 1995;68:105–130.
  • Facchinei F, Fischer A, Piccialli V. Generalized Nash equilibrium problems and Newton methods. Math Program. 2009;117:163–194.
  • Kesselman A, Leonardi S, Bonifaci V. Game-theoretic analysis of internet switching with selfish users. Lect Notes Comput Sci. 2005;3828:236–245.

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