Skip to main content
SpringerLink
Log in

A quadratically-convergent algorithm for general nonlinear programming problems

  • Published:
Mathematical Programming Submit manuscript

Abstract

This paper presents an algorithm for solving nonlinearly constrained nonlinear programming problems. The algorithm reduces the original problem to a sequence of linearly-constrained minimization problems, for which efficient algorithms are available. A convergence theorem is given which states that if the process is started sufficiently close to a strict second-order Kuhn—Tucker point, then the sequence produced by the algorithm exists and convergesR-quadratically to that point.

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. E.M.L. Beale, “Numerical methods,” in:Nonlinear programming, Ed. J. Abadie (North-Holland, Amsterdam, 1967) ch. 7.

    Google Scholar 

  2. A.R. Colville, “A comparative study on nonlinear programming codes,” IBM New York Scientific Center Report No. 320-2949, June, 1968.

  3. A.V. Fiacco and G.P. McCormick,Nonlinear programming: sequential unconstrained minimization techniques (Wiley, New York, 1968).

    Google Scholar 

  4. L.V. Kantorovich and G.P. Akilov,Functional analysis in normed spaces (Macmillan, New York, 1964).

    Google Scholar 

  5. G.P. McCormick, “A second-order method for the linearly constrained nonlinear programming problem,” in:Nonlinear programming, Eds. J.B. Rosen, O.L. Mangasarian and K. Ritter (Academic Press, New York, 1970) pp. 207–243.

    Google Scholar 

  6. G.P. McCormick, “Penalty function versus nonpenalty function methods for constrained nonlinear programming problems,”Mathematical Programming 1 (1971) 217–238.

    Google Scholar 

  7. J.M. Ortega and W.C. Rheinboldt,Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970).

    Google Scholar 

  8. K. Ritter, “A superlinearly convergent method for minimization problems with linear inequality constraints,” Technical Summary Report No. 1098. Mathematics Research Center, University of Wisconsin, Madison, 1971. To appear inMathematical Programming.

    Google Scholar 

  9. R.B. Wilson, “A simplicial method for convex programming,” Ph.D. Dissertation, Harvard University, 1963.

Download references

Author information

Authors and Affiliations

  1. University of Wisconsin, Madison, Wisconsin, USA

    Stephen M. Robinson

Authors
  1. Stephen M. Robinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Robinson, S.M. A quadratically-convergent algorithm for general nonlinear programming problems. Mathematical Programming 3, 145–156 (1972). https://doi.org/10.1007/BF01584986

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01584986

Keywords

Search

Navigation