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Articles

A Newton-type method for quasi-equilibrium problems and applications

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Pages 7-32 | Received 29 Nov 2019, Accepted 11 Jun 2021, Published online: 24 Jun 2021

References

  • Facchinei F, Kanzow C. Generalized Nash equilibrium problems. Ann Oper Res. 2010;175(1):177–211.
  • Nguyen TTV, Nguyen TPD, Strodiot JJ, et al. A class of hybrid methods for quasi-variational inequalities. Optim Lett. 2014;8(8):2211–2226.
  • Castellani M, Giuli M. A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces. J Glob Optim. 2019;75:163–176.
  • Castellani M, Giulli M, Pappalardo M. A Ky Fan minimax inequality for quasiequilibria on finite-dimensional spaces. Optim Theory Appl. 2018;179(1):53–64.
  • Cotrina J, Zúñiga J. A note on quasi-equilibrium problems. Oper Res Lett. 2018;46(1):138–140.
  • Aussel D, Cotrina J, Iusem A. An existence result for quasi-equilibrium problems. J Convex Anal. 2017;24(1):55–66.
  • Castellani M, Giulli M. An existence result for quasiequilibrium problems in separable Banach spaces. J Math Anal Appl. 2015;425(1):85–95.
  • Cubiotti P. Existence of solutions for lower semicontinuous quasi-equilibrium problems. Comput Math Appl. 1995;30(12):11–22.
  • Jacinto FMO, Scheimberg S. Duality for generalized equilibrium problem. Optimization. 2008;57(6):795–805.
  • Bigi G, Passacantando M. Gap functions for quasi-equilibria. J Global Optim. 2016;66(4):791–810.
  • Strodiot JJ, Nguyen TTV, Nguyen VH. A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems. J Global Optim. 2013;56(2):373–397.
  • Van NTT, Strodiot JJ, Nguyen VH, et al. An extragradient-type method for solving nonmonotone quasi-equilibrium problems. Optimization. 2018;67(5):651–664.
  • Santos PJS, Souza JCO. A proximal point method for quasi-equilibrium problems in Hilbert spaces. Optimization. 2020;1–16. doi:https://doi.org/10.1080/02331934.2020.1810686.
  • Bueno LF, Haeser G, Lara F, et al. An augmented Lagrangian method for quasi-equilibrium problems. Comput Optim Appl. 2020;76(3):737–766.
  • Santos PJS, Santos PSM, Scheimberg S. A proximal Newton-type method for equilibrium problems. Optim Lett. 2018;12(5):997–1009.
  • Outrata JV, Zowe J. A Newton method for a class of quasi-variational inequalities. Comput Optim Appl. 1995;4(1):5–21.
  • von Heusinger A, Kanzow C, Fukushima M. Newton's method for computing a normalized equilibrium in the generalized Nash game through fixed point formulation. Math Program. 2012;132:99–123.
  • Facchinei F, Kanzow C, Sagratella S. Solving quasi-variational inequalities via their KKT conditions. Math Program. 2014;144(1):369–412.
  • Facchinei F, Kanzow C, Karl S, et al. The semismooth Newton method for the solution of quasi-variational inequalities. Comput Optim Appl. 2015;62(1):85–109.
  • Hogan WW. Point-to-set maps in mathematical programming. SIAM Rev. 1973;15:591–603.
  • Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. Springer; 2003. (Springer Series in Operations Research; Vol. 1).
  • Izmailov AF, Solodov MV. Newton-type methods for optimization and variational problems. Springer; 2014. (Springer Series in Operations Research and Financial Engineering).
  • Sun D, Fukushima M, Qi L. Complementary and variational problems: state of the art. Philadelphia: SIAM; 1997. Chapter A computable generalized Hessian of the D-gap function and Newton-type methods for variational inequality problems; p. 452–472.
  • Dempe S, Vogel S. The generalized Jacobian of the optimal solution in parametric optimization. Optimization. 2001;50:387–405.
  • Ralph D, Dempe S. Directional derivatives of the solution of a parametric nonlinear program. Math Program. 1995;70(1):159–172.
  • Dreves A, Kanzow C. Nonsmooth optimization reformulations characterizing all solutions of jointly convex generalized Nash equilibrium problems. Comput Optim Appl. 2011;50(1):23–48.
  • Janin R. Directional derivative of the marginal function in nonlinear programming. Math Program Study. 1984;21:110–126.
  • Lang S. Undergraduate analysis. 2nd ed. Springer-Verlag New York; 1997. (Undergraduate Texts in Mathematics).
  • von Heusinger A, Kanzow C. Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Comput Optim Appl. 2009;43(3):353–377.
  • Facchinei F, Kanzow C, Sagratella S. Qvilib: a library of quasi-variational inequality test problems. Pacific J Optim. 2013;9(2):225–250.
  • Facchinei F, Kanzow C. Penalty methods for the solution of generalized Nash equilibrium problems. SIAM J Optim. 2010;20(5):2228–2253.

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