Variational Inequalities and Economic Equilibrium

Published Online:https://doi.org/10.1287/moor.1060.0233

References

  • Ahn B. H., Hogan W. W. W. On convergence of the PIES algorithm for computing equilibria. Oper. Res. (1982) 30:281–300LinkGoogle Scholar
  • Arrow K. J., Debreu G. Existence of an equilibrium for a competitive economy. Econometrica (1954) 22:265–290CrossrefGoogle Scholar
  • Auslender A., Teboulle M. Lagrangian duality and related multiplier methods for variational inequality problems. SIAM J. Optim. (2000) 10:1097–1115CrossrefGoogle Scholar
  • Auslender A., Teboulle M., Ben-Tiba S. A logarithmic-quadratic proximal method for variational inequalities. J. Comput. Optim. Appl. (1999) 645–668Google Scholar
  • Brézis H. Equations et inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Institut Fourier (1968) 18:115–175CrossrefGoogle Scholar
  • Brézis H. Problèmes unilatéraux. J. Math. Pures Appl. (1972) 51:1–168Google Scholar
  • Browder F. E. On the unification of the calculus of variations and the theory of monotone nonlinear operators in Banach spaces. Proc. Natl. Acad. Sci. (1966) 56:419–425CrossrefGoogle Scholar
  • Browder F. E. Existence and approximation of solutions of nonlinear variational inequalities. Proc. Natl. Acad. Sci. (1966) 56:1080–1086CrossrefGoogle Scholar
  • Browder F. E. Nonlinear maximal monotone operators in Banach space. Math. Ann. (1968) 175:89–113CrossrefGoogle Scholar
  • Browder F. E. Nonlinear variational inequalities and maximal monotone mappings in Banach spaces. Math. Ann. (1969) 183:213–231CrossrefGoogle Scholar
  • Brown D. J., DeMarzo P. M., Eaves C. Computing equilibria when asset markets are incomplete. Econometrica (1996) 64:1–27CrossrefGoogle Scholar
  • Chen G. H.-G., Rockafellar R. T. Convergence rates in forward-backward splitting. SIAM J. Optim. (1997) 7:421–444CrossrefGoogle Scholar
  • Codenotti B., Varadarajan K. Equilibrium for elastic exchange market: From nonlinear complementarity to convex programming. (2004) . Working paper, Department of Computer Science, University of Iowa, Iowa City, IowaGoogle Scholar
  • Crockett S., Spear S., Sunder S. Learning competitive equilibrium. Math. Econom. (2007) . ForthcomingGoogle Scholar
  • Dafermos S. Exchange price equilibria and variational inequalities. Math. Programming (1990) 46:391–402CrossrefGoogle Scholar
  • Debreu G.Theory of Value (1959) (Wiley, New York) Google Scholar
  • Debreu G. New concepts and techniques for equilibrium analysis. Mathematical Economics (1983) Econometric Soc. Monographs, No. 4Chap. 10Google Scholar
  • Dontchev A. D., Rockafellar R. T. Ample parameterization of variational inclusions. SIAM J. Optim. (2002) 12:170–187CrossrefGoogle Scholar
  • Eaves B. C., Schmedders K. General equilibrium theory and homotopy methods. J. Econom. Dynam. Control (1999) 23:1249–1279CrossrefGoogle Scholar
  • Esteban-Bravo M. Computing equilibria in general equilibrium models via interior point methods. Comput. Econom. (2004) 23:147–171CrossrefGoogle Scholar
  • Facchinei F., Pang J.-S.Finite-Dimensional Variational Inequalities and Complementarity Problems (2003) I and II(Springer-Verlag, New York) Springer Series in Operations ResearchGoogle Scholar
  • Ferris M. C., Sinapiromsaran K., Nguyen V. H., Strodiot J. J., Tossings P. Formulating and solving nonlinear programs as mixed complementary problems. Optimization. Lecture Notes in Economics and Mathematical Systems (2000) 481(Springer-Verlag)Google Scholar
  • Ferris M. C., Dirkse S. P., Meeraus A., Kehoe T. J., et al. Mathematical programming with equilibrium constraints: Automatic reformulation and solution via constrained optimization. Frontiers in Applied General Equilibrium Modeling (2005) (Cambridge University Press)67–94CrossrefGoogle Scholar
  • Florig M. On irreducible economies. Ann. d’Économ. de Statist. (2001) 61:184–199Google Scholar
  • Florig M. Hierarchic competitive equilibria. J. Math. Econom. (2001) 35:515–546CrossrefGoogle Scholar
  • Gale D.Theory of Linear Economic Models (1960) (McGraw-Hill, New York) Google Scholar
  • Glowinski R.Numerical Methods for Nonlinear Variational Problems (1984) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Glowinski R., Lions J.-L., Trémolières R.Numerical Analysis of Variational Inequalities (1981) (North-Holland, Amsterdam, The Netherlands) Google Scholar
  • Harker P. T., Pang J.-S. Finite-dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math. Programming, Ser. B (1990) 48:161–220CrossrefGoogle Scholar
  • Jain K. A polynomial time algorithm for computing the Arrow-Debreu market equilibrium for linear utilities. Proc. 43rd Annual IEEE Sympos. Foundations of Comput. Sci. (2004) 286–294Google Scholar
  • Jofre A., Rockafellar R. T., Wets R. J-B., Giannessi F., Maugeri A. A variational inequality scheme for determining an economic equilibrium. Variational Analysis and Applications (2005) (Kluwer)Google Scholar
  • Judd K. L., Kehoe Timothy J., Srinivasan T. N. Solving dynamical stochastic competitive general equilibrium models. Frontiers in Applied General Equilibrium Modeling (2005) (Cambridge University Press, Cambridge, UK) 45–66CrossrefGoogle Scholar
  • Judd K. L., Kubler F., Schmedders K., Dewatripont M., Hansen L., Turnovsky S. Computational methods for dynamic equilibria with heterogeneous agents. Advances in Economics and Econometrics (2003) (Cambridge University Press, Cambridge, UK) 243–290CrossrefGoogle Scholar
  • Kinderlehrer D., Stampacchia G.An Introduction to Variational Inequalities and Applications (1980) (Academic Press, New York) Google Scholar
  • Lions J.-L., Stampacchia G. Variational inequalities. Comm. Pure Appl. Math. (1967) 20:493–519CrossrefGoogle Scholar
  • Manne A. S. On the formulation and solution of economic equilibrium models. Math. Programming Stud. (1985) 23:1–20CrossrefGoogle Scholar
  • Mas-Colell A., Whinston M. D., Green J. R.Microeconomic Theory (1995) (Oxford University Press, Oxford, UK) Google Scholar
  • Mathiesen L. Computation of economic equilibria by a sequence of linear complementarity problems. Math. Programming Stud. (1985) 23:144–162CrossrefGoogle Scholar
  • Mathiesen L. Computational experience in solving equilibrium problems by a sequence of linear complementarity problems. Oper. Res. (1985) 33:1225–1250LinkGoogle Scholar
  • Mathiesen L. An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model: An example. Math. Programming (1987) 37:1–18CrossrefGoogle Scholar
  • Naniewicz Z., Panagiotopoulos P. D.Mathematical Theory of Hemivariational Inequalities and Applications (1995) (Marcel Dekker, New York) Google Scholar
  • Nomia O. Existence of Walras equilibria: The excess demand approach. (1996) . Working paper (series) Cahiers Maison Sci. Econom., University of Paris, Paris, FranceGoogle Scholar
  • Panagiotopoulos P. D.Inequality Problems in Mechanics and Applications (1985) (Birkhäuser, Boston, MA) CrossrefGoogle Scholar
  • Panagiotopoulos P. D.Hemivariational Inequalities: Applications in Mechanics and Engineering (1993) (Springer-Verlag, New York) CrossrefGoogle Scholar
  • Pang J.-S. Computing generalized Nash equilibria. Math. Programming, Ser. ATo appearGoogle Scholar
  • Pang J.-S., Fukushima M. Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games. Comput. Management Sci. (2005) 1:21–56CrossrefGoogle Scholar
  • Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) CrossrefGoogle Scholar
  • Rockafellar R. T. On the maximality of sums of nonlinear monotone operators. Trans. Amer. Math. Soc. (1970) 149:75–88CrossrefGoogle Scholar
  • Rockafellar R. T.Conjugate Duality and Optimization. No. 16, Conference Board of Math. Sciences Series (1974) (SIAM Publications)CrossrefGoogle Scholar
  • Rockafellar R. T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. (1976) 14:877–898CrossrefGoogle Scholar
  • Rockafellar R. T.Network Flows and Monotropic Optimization (1998) (Athena Scientific, Nashua, NH) . Originally published by Wiley 1983, and republished by Athena Scientific 1998Google Scholar
  • Rockafellar R. T., Wets R. J-B.Variational Analysis (1997) (Springer-Verlag, Berlin, Germany) Google Scholar
  • Scarf H. E. The approximate fixed points of a continuous mapping. SIAM J. Appl. Math. (1967) 15:1328–1343CrossrefGoogle Scholar
  • Scarf H. E.The Computation of Economic Equilibria (1973) (Yale University Press, New Haven, CT) Google Scholar
  • Todd M. J.Computation of Fixed Points and Applications. Lecture Notes in Econom. Math. Systems 124 (1976) (Springer-Verlag, Berlin, Germany) CrossrefGoogle Scholar
  • Varian H. R.Microeconomic Analysis (1992) (Norton, New York) Google Scholar
  • Ye Y.-Y. A path to the Arrow-Debreu competitive market equilibrium. Math. ProgrammingForthcomingGoogle Scholar
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