Exact Penalization of Generalized Nash Equilibrium Problems
Published Online:16 Sep 2020https://doi.org/10.1287/opre.2019.1942
References
- (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290.Crossref, Google Scholar
- (1976) Optimisation: Méthodes Numériques (Masson, Paris).Google Scholar
- (2017) Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality. Math. Methods Oper. Res. 85(1):3–18.Crossref, Google Scholar
- (2018) A general equilibrium model for transportation systems with e-hailing services and flow congestion. Transportation Res. Part B 129:273–304.Google Scholar
- (2002) Allocation of railroad capacity under competition: A game theoretic approach to track time pricing. Gendreau M, Marcotte P, eds. Transportation and Network Analysis: Current Trends (Springer, Boston), 1–17.Google Scholar
- (1999) Strong conical hull intersection property, bounded linear regularity, Jameson’s property (G), and error bounds in convex optimization. Math. Programming 86(1):135–160.Crossref, Google Scholar
- (2006) A game-theoretic formulation of joint implementation of environmental projects. Eur. J. Oper. Res. 168(1):221–239.Crossref, Google Scholar
- (2012) A line search exact penalty method using steering rules. Math. Programming 133(1–2):39–73.Crossref, Google Scholar
- (2006) Knitro: An integrated package for nonlinear optimization. Di Pillo G, Roma M, eds. Large-Scale Nonlinear Optimization, Nonconvex Optimization and Its Applications, vol. 83 (Springer, Boston), 35–59.Google Scholar
- (2008) Steering exact penalty methods for nonlinear programming. Optim. Methods Software 23(2):197–213.Crossref, Google Scholar
- (1990) Optimization and Nonsmooth Analysis, Classics in Applied Mathematics, vol. 5 (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
- (2012) Modern Optimization Modeling Techniques (Birkhäuser, Basel, Switzerland).Crossref, Google Scholar
- (1952) A social equilibrium existence theorem. Proc. Natl. Acad. Sci. USA 38(10):886–893.Crossref, Google Scholar
- (1998) Exact penalization via Dini and Hadamard conditional derivatives. Optim. Methods Software 9(1–3):19–36.Crossref, Google Scholar
- (1989) Exact penalty functions for nondifferentiable programming problems. Clarke FH, Dem’yanov VF, Giannessi F, eds. Nonsmooth Optimization and Related Topics (Springer, Boston), 89–107.Crossref, Google Scholar
- (1992) Regularity conditions and exact penalty functions in Lipschitz programming problems. Nonsmooth Optimization Methods and Applications (Gordon and Breach Science Publishers, London), 107–120.Google Scholar
- (1995) Exact barrier function methods for Lipschitz programs. Appl. Math. Optim. 32(1):1–31.Crossref, Google Scholar
- (1989) Exact penalty functions in constrained optimization. SIAM J. Control Optim. 27(6):1333–1360.Crossref, Google Scholar
- (2017) Computing all solutions of linear generalized Nash equilibrium problems. Math. Methods Oper. Res. 85(2):207–221.Crossref, Google Scholar
- (2010a) Generalized Nash equilibrium problems. Ann. Oper. Res. 175(1):177–211.Crossref, Google Scholar
- (2010b) Penalty methods for the solution of generalized Nash equilibrium problems. SIAM J. Optim. 20(5):2228–2253.Crossref, Google Scholar
- (2011) Partial penalization for the solution of generalized Nash equilibrium problems. J. Global Optim. 50(1):39–57.Crossref, Google Scholar
- (2006) Exact penalty functions for generalized Nash problems. Large-Scale Nonlinear Optimization, Nonconvex Optimization and Its Applications, vol. 83 (Springer, Boston), 115–126.Crossref, Google Scholar
- (2007) Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer Science & Business Media, New York).Google Scholar
- (2009) Nash equilibria: The variational approach. Palomar DP, Eldar YC, eds. Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, UK), 443–493.Google Scholar
- (2011) On the computation of all solutions of jointly convex generalized Nash equilibrium problems. Optim. Lett. 5(3):531–547.Crossref, Google Scholar
- (2007) On generalized Nash games and variational inequalities. Oper. Res. Lett. 35(2):159–164.Crossref, Google Scholar
- (1990) Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Classics in Applied Mathematics, vol. 4 (Society for Industrial and Applied Mathematics, Philadelphia).Crossref, Google Scholar
- (2014) Generalized Nash equilibrium problems-recent advances and challenges. Pesquisa Operacional 34(3):521–558.Crossref, Google Scholar
- (2011) Restricted generalized Nash equilibria and controlled penalty algorithm. Comput. Management Sci. 8(3):201–218.Crossref, Google Scholar
- (1979) Exact penalty functions in nonlinear programming. Math. Programming 17(1):251–269.Crossref, Google Scholar
- (1991) Generalized Nash games and quasi-variational inequalities. Eur. J. Oper. Res. 54(1):81–94.Crossref, Google Scholar
- (2007) Nash-cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints. Oper. Res. 55(1):113–127.Link, Google Scholar
- (1999) Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices. Oper. Res. 47(1):102–112.Link, Google Scholar
- (2016) Augmented Lagrangian methods for the solution of generalized Nash equilibrium problems. SIAM J. Optim. 26(4):2034–2058.Crossref, Google Scholar
- (2018) Augmented Lagrangian and exact penalty methods for quasi-variational inequalities. Comput. Optim. Appl. 69(3):801–824.Crossref, Google Scholar
- (1999) Asymptotic constraint qualifications and global error bounds for convex inequalities. Math. Programming 84(1):137–160.Crossref, Google Scholar
- (2007) Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems. Comput. Management Sci. 4(2):183–204.Crossref, Google Scholar
- (2005) Coupled constraint Nash equilibria in environmental games. Resource Energy Econom. 27(2):157–181.Crossref, Google Scholar
- (2000) Relaxation algorithms to find Nash equilibria with economic applications. Environ. Model. Assessment 5(1):63–73.Crossref, Google Scholar
- (2012) On the variational equilibrium as a refinement of the generalized Nash equilibrium. Automatica 48(1):45–55.Crossref, Google Scholar
- (1998) Error bounds for convex inequality systems. Generalized Convexity, Generalized Monotonicity: Recent Results (Springer, Boston), 75–110.Crossref, Google Scholar
- (2011) Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints. Comput. Optim. Appl. 48(3):423–452.Crossref, Google Scholar
- (2004) Regularities and their relations to error bounds. Math. Programming 99(3):521–538.Crossref, Google Scholar
- (1955) Note on non-cooperative convex games. Pacific J. Math. 5(Suppl. 1):807–815.Crossref, Google Scholar
- (1997) Error bounds in mathematical programming. Math. Programming 79(1–3):299–332.Crossref, Google Scholar
- (2005) Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Management Sci. 2(1):21–56.Crossref, Google Scholar
- (2008) Distributed power allocation with rate constraints in Gaussian parallel interference channels. IEEE Trans. Inform. Theory 54(8):3471–3489.Crossref, Google Scholar
- (2010) Design of cognitive radio systems under temperature-interference constraints: A variational inequality approach. IEEE Trans. Signal Processing 58(6):3251–3271.Crossref, Google Scholar
- (1991) An implicit-function theorem for a class of nonsmooth functions. Math. Oper. Res. 16(2):292–309.Link, Google Scholar
- (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3):520–534.Crossref, Google Scholar
- (2013) On the solution of affine generalized Nash equilibrium problems with shared constraints by Lemke’s method. Math. Programming 142(1–2):1–46.Crossref, Google Scholar
- (2018) The noncooperative transportation problem and linear generalized Nash games. Eur. J. Oper. Res. 266(2):543–553.Crossref, Google Scholar
- (2001) Convergence of a block coordinate descent method for nondifferentiable minimization. J. Optim. Theory Appl. 109(3):475–494.Crossref, Google Scholar
- (1994) On relaxation algorithms in computation of noncooperative equilibria. IEEE Trans. Automatic Control 39(6):1263–1267.Google Scholar
- (2009) Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions. Comput. Optim. Appl. 43(3):353–377.Crossref, Google Scholar

