Skip to main content
Log in

A nonsmooth Newton method for variational inequalities, II: Numerical results

  • Published:
Mathematical Programming Submit manuscript

Abstract

This paper presents the results of extensive computational testing of the modified damped Newton algorithm for solving variational inequality problems presented in Part I [8].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. D.P. Bertsekas and E.M. Gafni, “Projection methods for variational inequalities with application to the traffic assignment problem,”Mathematical Programming Study 17 (1982) 139–159.

    Google Scholar 

  2. P.T. Harker, “Alternative models of spatial competition,”Operations Research 34 (1986) 410–425.

    Google Scholar 

  3. P.T. Harker, “Accelerating the convergence of the diagonalization and projection algorithms for finitedimensional variational inequalities,”Mathematical Programming 41 (1988) 29–59.

    Google Scholar 

  4. P.T. Harker, “Dispersed spatial price equilibrium,”Environment and Planning A 20 (1988) 353–368.

    Google Scholar 

  5. P.T. Harker and J.S. Pang, “A damped-Newton method for the linear complementarity problem,” in: G. Allgower and K. Georg, ed.,AMS Transactions on Applied Mathematics 26 (1990) 265–284.

    Google Scholar 

  6. P.T. Harker and J.S. Pang, “Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications,”Mathematical Programming B 48 (1990) 1–60.

    Google Scholar 

  7. P.T. Harker and B. Xiao, “Newton's method for the nonlinear complementarity problem: a B-differentiable equation approach,”Mathematical Programming 48 (1990) 339–357.

    Google Scholar 

  8. B. Xiao and P.T. Harker, “A nonsmooth Newton method for variational inequalities, I: theory,”Mathematical Programming 65 (1994) 151–194.

    Google Scholar 

  9. D.M. Himmelblau,Applied Nonlinear Programming (McGraw-Hill, Inc., 1972).

  10. N.H. Josephy, “Newton's method for generalized equations,” Technical Report No. 1965, Mathematics Research Center, University of Wisconsin (Madison, WI, 1979).

    Google Scholar 

  11. J. MacKinnon, “A technique for the solution of spatial equilibrium models,”Journal of Regional Science 16 (1976) 293–307.

    Google Scholar 

  12. L. Mathiesen, “Computation of economic equilibria by a sequence of linear complementarity problems,”Mathematical Programming Study 23 (1985) 144–162.

    Google Scholar 

  13. L. Mathiesen, “Computational experience in solving equilibrium models by a sequence of linear complementarity problems,”Operations Research 33 (1985) 1225–1250.

    Google Scholar 

  14. K.G. Murty,Linear Complementarity, Linear and Nonlinear Programming (Helderman-Verlag, Berlin, 1988).

    Google Scholar 

  15. M.J.D. Powell, “A method for nonlinear constraints in minimization problems,” in: R. Fletcher, ed.,Optimization (Academic Press, New York, 1969).

    Google Scholar 

  16. J. Rowse, “On the solution of spatial equilibrium models,”Decision Sciences 13 (1982) 619–637.

    Google Scholar 

  17. T. Rutherford, “Applied general equilibrium modeling,” Ph.D. dissertation, Department of Operations Research, Stanford University (Stanford, CA, 1986).

    Google Scholar 

  18. H.E. Scarf and T. Hansen,Computation of Economic Equilibria (Yale University Press, New Haven, Connecticut, 1973).

    Google Scholar 

  19. R.L. Tobin, “A variable dimension solution approach for the general spatial price equilibrium problem,”Mathematical Programming 40 (1988) 33–51.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Corresponding author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xiao, B., Harker, P.T. A nonsmooth Newton method for variational inequalities, II: Numerical results. Mathematical Programming 65, 195–216 (1994). https://doi.org/10.1007/BF01581696

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01581696

Keywords

Navigation