Skip to main content
SpringerLink
Log in

An NE/SQP Method for the Bounded Nonlinear Complementarity Problem

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

NE/SQP (Refs. 2–3) is a recent algorithm that has proven quite effective for solving the nonlinear complementarity problem (NCP). NE/SQP is robust in the sense that its direction-finding subproblems are always solvable; in addition, the convergence rate of this method is q-quadratic. In this note, we consider a generalized version of NE/SQP, as first described in Ref. 4, which is suitable for the bounded NCP. We extend the work in Ref. 4 by demonstrating a stronger convergence result and present numerical results on test problems.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gabriel, S. A., Algorithms for the Nonlinear Complementarity Problem: The NE/SQP Method and Extensions, PhD Thesis, Johns Hopkins University, 1992.

  2. Pang, J. S., and Gabriel, S. A., NE/SQP: A Robust Algorithm for the Nonlinear Complementarity Problem, Mathematical Programming, Vol. 60, pp. 295–337, 1993.

    Google Scholar 

  3. Gabriel, S. A., and Pang, J. S., An Inexact NE/SQP Method for Solving the Nonlinear Complementarity Problem, Computational Optimization and Applications, Vol. 1, pp. 67–91, 1992.

    Google Scholar 

  4. Pang, J. S., and Qi, L., Nonsmooth Equations: Motivation and Algorithms, SIAM Journal on Optimization, Vol. 3, pp. 443–465, 1993.

    Google Scholar 

  5. Gill, P. E., Murray, W., and Saunders, M. A., User's Guide for QPOPT 1.0: A FORTRAN Package for Quadratic Programming, Department of Mathematics, University of California, San Diego, California, 1995.

    Google Scholar 

  6. Murphy, F. H., Sherali, H. D., and Soyster, A. L., A Mathematical Programming Approach for Determining Oligopolistic Market Equilibrium, Mathematical Programming, Vol. 24, pp. 92–106, 1982.

    Google Scholar 

  7. Hock, W., and Schittkowski, K., Test Examples for Nonlinear Programming Codes, Springer Verlag, Berlin, Germany, 1981.

    Google Scholar 

  8. Friesz, T. L., Tobin, R. L., Smith, T. E., and Harker, P. T., A Nonlinear Complementarity Formulation and Solution Procedure for the General Derived Demand Network Equilibrium Problem, Journal of Regional Science, Vol. 23, pp. 337–359, 1983.

    Google Scholar 

  9. Aashtiani, H. Z., The Multi-Modal Traffic Assignment Problem, PhD Thesis, Sloan School of Management, Massachusetts Institute of Technology, 1979.

  10. Aashtiani, H. Z., and Magnanti, T. L., Equilibria on a Congested Transportation Network, SIAM Journal on Algebraic and Discrete Methods, Vol. 2, pp. 213–226, 1981.

    Google Scholar 

  11. De Luca, T., Facchinei, F., and Kanzow, C., A Semismooth Equation Approach to the Solution of Nonlinear Complementarity Problems, Mathematical Programming, Vol. 75, pp. 407–439, 1996.

    Google Scholar 

  12. Billups, S. C., and Ferris, M., QPCOMP: A Quadratic Programming Based Solver for Mixed Complementarity Problems, Vol. 76, pp. 533–562, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ICF Kaiser International, Fairfax, Virginia

    S. A. Gabriel (Project Manager)

Authors
  1. S. A. Gabriel
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gabriel, S.A. An NE/SQP Method for the Bounded Nonlinear Complementarity Problem. Journal of Optimization Theory and Applications 97, 493–506 (1998). https://doi.org/10.1023/A:1022643104274

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022643104274

Search

Navigation