Advertisement

Demand Homotopies for Computing Nonlinear and Multi-Commodity Spatial Equilibria

  • Philip C. Jones
  • Romesh Saigal
  • Michael Schneider
Conference paper
  • 45 Downloads
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 249)

Abstract

This paper examines the problem of computing nonlinear and multi-commodity spatial equilibria. With mild assumptions on excess demand functions (neither differentiability nor convexity assumptions need hold), we show that a direct pivoting procedure will compute an equilibrium.

Keywords

Complementarity Problem Excess Demand Node Problem Market Clearing Condition Single Commodity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Asmuth, B.C. Eaves, and E.L. Peterson, “Computing economic equilibria on affine networks with Lemke’s algorithm”, Mathematics of Operations Research 4(1979)209–214.CrossRefGoogle Scholar
  2. [2]
    S. Dafermos, “An iterative scheme for variational inequalities”, Mathematical Programming 26(1983)40–47.CrossRefGoogle Scholar
  3. [3]
    B.C. Eaves, “A locally quadratically convergent algorithm for computing stationary points”, TR-SOL 78-13, Department of Operations Research, Stanford University(Stanford, CA, 1978).Google Scholar
  4. [4]
    S. Enke, “Equilibrium among spatially separated markets: solution by electric analogue”, Econometrica 19(1951)40–47.CrossRefGoogle Scholar
  5. [5]
    S.C. Fang, “An iterative method for generalized complementarity problems”, Mathematics Research Report 79-11, Department of Mathematics, University of Maryland(Cantonsville, MD, 1979).Google Scholar
  6. [6]
    C.R. Glassey, “A quadratic network optimizatin model for equilibrium single commodity trade flows”, Mathematical Programming 14(1978)98–107.CrossRefGoogle Scholar
  7. [7]
    P.C. Jones, R. Saigal, and M. Schneider, “A variable dimension homotopy for computing spatial equilibria”, Operations Research Letters 3(1984)19–24.CrossRefGoogle Scholar
  8. [8]
    P.C. Jones, R. Saigal, and M. Schneider, “Computing nonlinear network equilibria”, Mathematical Programming 31(1985)57–66.CrossRefGoogle Scholar
  9. [9]
    P.C. Jones, R. Saigal, and M. Schneider, “A variable dimension homotopy on networks for computing linear spatial equilibria”, to appear in Discrete Applied Mathematics.Google Scholar
  10. [10]
    N. Josephy, “Newton’s method for generalized equations”, TSR 1966, Mathematics Research Center, University of Wisconsin(Madison, WI, 1979).Google Scholar
  11. [11]
    L. Mathiesen, “A linear complementarity approach to general equilibrium”, TR-SOL 74-9, Systems Optimization Laboratory, Stanford University(Stanford, CA, 1974).Google Scholar
  12. [12]
    J.S. Pang and D. Chan, “Iterative methods for variational and complementarity problems”, Mathematical Programming 24 (1982)284–313.CrossRefGoogle Scholar
  13. [13]
    J.S. Pang and P.S.C. Lee, “A parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model”, Mathematical Programing 20(1981)81–102.CrossRefGoogle Scholar
  14. [14]
    R. Saigal, “A homotopy for solving large, sparse, and structured fixed point problems”, Mathematicals of Operations Research 8 (1983)557–578.CrossRefGoogle Scholar
  15. [15]
    P. Samuelson, “Spatial price equilibrium and linear programming”, American Economic Review 42(1952)283–303.Google Scholar
  16. [16]
    M. Schneider, “Single-commodity spatial equilibria: a network complementarity approach”,Ph.D. Thesis, Northwestern University (Evanston, IL, 1984).Google Scholar
  17. [17]
    T. Takayama and G. Judge, Spatial and temporal price and allocation models (North-HoHand, Amsterdam, 1971).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Philip C. Jones
    • 1
  • Romesh Saigal
    • 1
  • Michael Schneider
    • 2
  1. 1.Department of Industrial Engineering and Management ScienceTechnological Institute Northwestern UniversityEvanstonUSA
  2. 2.Department of Civil EngineeringPrinceton UniversityPrincetonUSA

Personalised recommendations