Computing equilibria in general equilibrium models via interior-point methods

Computational Economics

Volumn 23, Issue 2, 2004, Pages 147-171

  Esteban Bravo, Mercedes ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Computation of equilibria; General equilibrium; Interior point methods

Indexed keywords

EID: 26844509991     PISSN: 09277099     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:CSEM.0000021673.38534.ef     Document Type: Article

References (64)

1. Adelman, I. and Robinson, S. (1978). Income Distribution Policy in Developing Countries: A Case Study of Korea. Stanford University Press, Stanford, CA.
2. Arrow, K.J. and Debreu, G. (1954). Existence of equilibrium for a competitive economy. Econometrica, 22, 265-290.
3. Arrow, K.J. and Hahn, F.H. (1971, 1983). General Competitive Analysis. Advanced Textbooks in Economics, Vol. 12. North Holland, New York.
4. Brouwer, L.E. (1912). Über Abbildung von Mannigfaltigkeiten. Math. Ann., 71, 97-115.
5. Byrd, R.H., Hribar, M.E. and Nocedal, J. (1999). An interior point algorithm for large-scale nonlinear programming. SIAM Journal on Optimization, 9(4), 877-900.
6. Cottle, R.W. (1966). Nonlinear programs with positively bounded jacobians. SIAM Journal on Applied Mathematics, 14, 147-158.
7. Debreu, G. (1959, 1987). Theory of Value. In 1959, John Wiley and Sons, New York. Second edition in 1987, Cowless Foundation Monographs, 17, Yale University Press, New Haven.
8. Dennis, J.E. Jr. and Schnabel, R.B. (1996). Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia.
9. Diewert, W.E. (1970). On a theorem of Negishi. Metroeconomica, XXV, 119-135.
10. Dirkse, S.P. and Ferris, M.C. (1995). The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software, 5, 123-156.
11. Dirkse, S.P. and Ferris, M.C. (1997). Crash techniques for large-scale complementarity problems. In M.C. Ferris and J.S. Pang (eds.), Complementarity and Variational Problems: State of the Art. SIAM Publications, Philadelphia, Pennsylvania.
12. Eaves, B.C. (1972). Homotopies for the computation of fixed points. Mathematical Pogramming, 3, 225-237.
13. Eaves, B.C. and Schmedders, K. (1999). General equilibrium models and homotopy methods. Journal of Economic Dynamics and Control, 23, 1249-1279.
14. Esteban-Bravo, M. (2000). Existence and computation of equilibria in general equilibrium. Ph.D. thesis, Universidad Carlos III de Madrid, Spain, December.
15. Ferris, M.C., Kanzow, C. and Munson, T. (1999). Feasible descent algorithms for mixed complementarity problems. Mathematical Programming, 86, 475-497.
16. Fiacco, A.V. and McCormick, G.P. (1968). Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley and Sons, New York.
17. Fletcher, R. (1987). Practical Methods of Optimization, 2nd edn. Wiley, Chichester.
18. Gale, D. (1955). The law of supply and demand. Mathematica Scandinavia, 3, 155-169.
19. Garcia, C.B. and Zangwill, W.I. (1981). Pathways to Solutions, Fixed Points, and Equilibria. Prentice Hall, Englewood Cliffs, NJ.
20. Gill, P.E., Murray, W., Sauders, M.A., Tomlin, J.A. and Wright, M.H. (1986). On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method. Mathematical Programming, 36, 183-209.
21. Ginsburgh, V. and Keyzer, M. (1997). The Structure of Applied General Equilibrium Models. The MIT Press, Cambridge.
22. Ginsburgh, V. and Waelbroeck, J.L. (1981). Activity Analysis and General Equilibrium Modelling. North-Holland, Amsterdam.
23. Golub, G.H. and Van Loan, C.F. (1996). Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore.
24. Hansen, T. (1968). On the approximation of a competitive equilibrium. Ph.D. thesis, Yale University.
25. Harker, P.T. and Pang, J.S. (1990). Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Mathematical Programming, 48, 161-220.
26. Hirsch, M.W. (1963). A proof of the nonretractability of a cell into its boundary. Proceedings of the American Mathematical Society, 14, 364-365.
27. Judd, K.L. (1998). Numerical Methods in Economics. The MIT Press, Cambridge.
28. Kehoe, T.J. (1991). Computation and multiplicity of equilibria. In W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, Vol. IV, Ch. 38, 2049-2144. Elsevier Science Publishers B.V.
29. Kellog, R.B., Li, T.Y. and Yorke, J. (1976). A constructive proof of the Brouwer fixed-point theorem and computational results. SIAM Journal of Numerical Analysis, 13, 478-483.
30. Kuhn, H.W. (1968). Simplicial approximation of fixed points. Proc. Nat. Acad. Sci., 61, 1238-1242.
31. Kuhn, H.W. (1969). Approximate search for fixed points. In Computing Methods in Optimization Problems-2. Academic Press, New York.
32. Lemke, C.E. (1965). Bi-matrix equilibrium points and mathematical programing. Management Science, 11, 681-689.
33. Lemke, C.E. and Howson, J.T. (1964). Equilibrium points of bi-matrix games. SIAM Journal of Applied Mathematics, 12, 412-423.
34. Luenberger, D.G. (1979). Introduction to Dynamic Systems: Theory, Models, and Applications. Wiley, New York.
35. Mantel, R.R. (1971). The welfare adjustment process: its stability properties. International Economic Review, 12, 415-430.
36. Mathiesen, L. (1985). Computational experience in solving equilibrium models by a sequence of linear complementarity problems. Operations Research, 33(6), 1225-1250.
37. Merril, O.H. (1972). Applications and extension of an algorithm that computes fixed points of certain upper semi-continuous point to set mappings. Ph.D. thesis, Department of Industrial Engineering, University of Michigan.
38. McKenzie, L. (1959). On the existence of general equilibrium for a competitive market. Econometrica, 27, 54-71.
39. Morales, J.L., Waltz, R., Liu, G., Goux, J.P. and Nocedal, J. (2001). Assessing the potential of interior methods for nonlinear optimization. Proceedings of the first Sandia workshop on large-scale PDE-constrained optimization. In O. Ghattas (ed.), Springer's Lecture Notes in Computational Science and Engineering. Santa Fe, New Mexico, U.S.A.
40. Nagurney, A. (1993). Network Economies - A Variational Inequality Approach. Kluwer Academic Publishers, Dordrecht, The Netherlands.
41. Negishi, T. (1960). Welfare economics and the existence of an equilibrium for a competitive economy. Metroeconomica, XII, 92-97.
42. Nikaido, H. (1956). On the classical multilateral exchange problem. Metroeconomica, VIII, 135-145.
43. Nesterov, Y. and Nemirovskii, A. (1994). Interior-Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia.
44. Nocedal, J. and Wright, S.J. (1999). Numerical Optimization. Springer Series in Operations Research. Springer-Verlag, New York.
45. Ortega, J.M. and Rheinboldt, W.C. (1970). Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, San Diego.
46. Robinson, S.M. (1994). Newton's method for a class of nonsmooth functions. Set-Valued Analysis, 2, 291-305.
47. Samuelson, P.A. (1941). The stability of equilibrium: comparative statics and dynamics. Econometrica, 9, 97-120.
48. Samuelson, P.A. (1942). The stability of equilibrium: linear and nonlinear systems. Econometrica, 10, 1-25.
49. Samuelson, P.A. (1947). Foundations of Economic Analysis. Harvard University Press, Cambridge, Mass.
50. Scarf, H.E. (1967). The approximation of fixed points of a continuous mapping. Journal of Applied Mathematics, 15, 1328-1343.
51. Scarf, H.E. (1982). The computation of equilibrium prices: an exposition. In W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, Vol. II, Ch. 21, 1007-1061. Elsevier Science Publishers B.V.
52. Scarf, H.E. (1998). The computation of equilibrium prices. In A. Kirman (ed.), Elements of General Equilibrium Analysis, Ch. 4, 88-138. Blackwell Publishers Ltd.
53. Scarf, H.E. and Hansen, T. (1973). The Computation of Economic Equilibria. Yale University Press, New Haven.
54. Smale, S. (1974-76). Global analysis and economics, IIA-VI. Journal of Mathematical Economics, 1, 1-14, 107-117, 119-127, 213-221.
55. Smale, S. (1976). A convergent process of price adjustment and global Newton methods. Journal of Mathematical Economics, 3, 1-14.
56. Smale, S. (1982). Global analysis and economics. In W. Hildenbrand and H. Sonnenschein (eds.), Handbook of Mathematical Economics, Vol. I, Ch. 8, 331-370. Elsevier Science Publishers B.V.
57. Sperner, E. (1928). Neuer Beweis für die Invarianz der Dimensionszahl und des Gebietes. Abh. a.d. Math. Sem. d. Univ. Hamburg, 6, 265-272.
58. Takayama, A. and El Hodiri, M. (1968). Programming, Pareto optimum and the existence of competitive equilibria. Metroeconomica, XX, 1-10.
59. Van der Laan, G. and Talman, A.J.J. (1979). A restart algorithm for computing fixed points without an extra dimension. Mathematical Programming, 17, 74-84.
60. Walras, L. (1874, 1954). Eléments d'économie politique pure. In 1874, L. Corbaz, Lausanne.
61. English translation of William Jaffé in 1954: Elements of Pure Economics. Allen and Unwin, London.
62. Whalley, J. (1973). A numerical assessment of the 1973 United Kingdom. Ph.D. thesis, Yale University.
63. Wright, M.H. (1991). Interior methods for constrained optimization. Acta Numerica, 341-407.
64. Wright, S. (1997). Primal-Dual Interior-Point Methods. SIAM Philadelphia, PA.