Skip to main content

NLPQL: A fortran subroutine solving constrained nonlinear programming problems

Abstract

NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.

This is a preview of subscription content, access via your institution.

References

  1. J. Abadie, Méthode du gradient reduit generalisé: Le code GRGA, Note HI 1756/00, Electricite de France, Paris (1975).

    Google Scholar 

  2. R.M. Chamberlain, C. Lemarechal, H.C. Pedersen and M.J.D. Powell, The watchdog technique for forcing convergence in algorithms for constrained minimization, Mathematical Programming Studies 16(1982)1.

    Google Scholar 

  3. R.L. Crane, B.S. Garbow, K.E. Hillstrom and M. Minkoff, LCLSQ: An implementation of an algorithm for linearly constrained linear least squares problems, Report ANL-80-116, Argonne National Laboratory, Argonne, Illinois (1980).

    Google Scholar 

  4. R.L. Crane, K.E. Hillstrom and M. Minkoff, Solution of the general nonlinear programming problem with subroutine VMCON, Report ANL-80-64, Argonne National Laboratory, Argonne, Illinois (1980).

    Google Scholar 

  5. A.V. Fiacco and G.P. McCormick,Nonlinear Sequential Unconstrained Minimization Techniques (Wiley, New York, 1968).

    Google Scholar 

  6. R. Fletcher, A FORTRAN program for general quadratic programming, Report No. R6370, AERE, Harwell, Berkshire (1970).

    Google Scholar 

  7. R. Fletcher, An ideal penalty function for constrained optimization, in:Nonlinear Programming 2, ed. O.L. Mangasarian, R.R. Meyer and S.M. Robinson (Academic Press, New York, 1975).

    Google Scholar 

  8. P.E. Gill, W. Murray and M.A. Saunders, Methods for computing and modifying the LDV factors of a matrix, Mathematics of Computation 29(1975)1051.

    Google Scholar 

  9. P.E. Gill, W. Murray, M.A. Saunders and M.H. Wright, Two steplength algorithms for numerical optimization, Report SOL 79-25, Dept. of Operations Research, Stanford University, Stanford (1979).

    Google Scholar 

  10. P.E. Gill, W. Murray, M.A. Saunders and M. Wright, User's guide for SOL/QPSOL: A FORTRAN package for quadratic programming, Report SOL 82-7, Dept. of Operations Research, Stanford University (1982).

  11. P.E. Gill, W. Murray, M.A. Saunders and M. Wright, User's guide for SOL/NPSOL: A FORTRAN package for nonlinear programming, Report SOL 83-12, Department of Operations Research, Stanford University (1983).

  12. S.-P. Han, Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Mathematical Programming 11(1976)263.

    Google Scholar 

  13. S.-P. Han, A globally convergent method for nonlinear programming, J. of Optimization Theory and Applications 22(1977)297.

    Google Scholar 

  14. W. Hock and K. Schittkowski,Test Examples for Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 187 (Springer-Verlag, Berlin — Heidelberg — New York, 1981).

    Google Scholar 

  15. W. Hock and K. Schittkowski, A comparative performance evaluation of 27 nonlinear programming codes, Computing 30(1983)335.

    Google Scholar 

  16. W. Kribbe, Documentation of the FORTRAN-subroutines for quadratic programming CONQUA and START, Report 8231/1, Econometric Institute, Erasmus University, Rotterdam (1982).

    Google Scholar 

  17. L.S. Lasdon and A.D. Waren, Generalized reduced gradient software for linearly and nonlinearly constrained problems, in:Design and Implementation of Optimization Software, ed. H.J. Greenberg (Sijthoff and Noordhoff, Alphen aan den Rijn (1978).

  18. C.L. Lawson and R.J. Hanson,Solving Least Squares Problems (Prentice Hall, Englewood, Cliffs, New Jersey, 1974).

    Google Scholar 

  19. D.A. Pierre and M.J. Lowe,Mathematical Programming via Augmented Lagrangians (Addison-Wesley, Reading, Massachusetts, 1975).

    Google Scholar 

  20. M.J.D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in:Numerical Analysis, ed..A. Watson,Lecture Notes in Mathematics, Vol. 630 (Springer-Verlag, Berlin — Heidelberg — New York, 1978).

    Google Scholar 

  21. M.J.D. Powell, The convergence of variable metric methods for nonlinearly constrained optimization calculations, in:Nonlinear Programming 3, ed. O.L. Mangasarian, R.R. Meyer and S.M. Robinson (Academic Press, New York — San Francisco — London, 1978).

    Google Scholar 

  22. M.J.D. Powell, VMCWD: A FORTRAN subroutine for constrained optimization, Report DAMTP 1982/NA4, University of Cambridge, Cambridge (1982).

    Google Scholar 

  23. M.J.D. Powell, ZQPCVX: A FORTRAN subroutine for convex quadratic programming, Report DAMTP 1983/NA17, University of Cambridge, Cambridge (1983).

    Google Scholar 

  24. M.J.D. Powell, The performance of two subroutines for constrained optimization on some difficult test problems, Report DAMTP 1984/NA6, University of Cambridge, Cambridge (1984).

    Google Scholar 

  25. D. Rufer, User's guide for NLP — A subroutine package to solve nonlinear optimization problems, Report No. 78-07, Fachgruppe für Automatik, ETH Zürich (1978).

    Google Scholar 

  26. K. Schittkowski,Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 183 (Springer-Verlag, Berlin — Heidelberg — New York, 1980).

    Google Scholar 

  27. K. Schittkowski, The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function. Part 1: Convergence analysis, Numerische Mathematik 38(1981)83.

    Google Scholar 

  28. K. Schittkowski, On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function, Mathematische Operationsforschung und Statistik, Ser. Optimization 14(1983)197.

    Google Scholar 

  29. K. Schittkowski, User's guide for the nonlinear programming code NLPQL, Report, Institut für Informatik, Universität Stuttgart, FRG (1984).

    Google Scholar 

  30. K. Schittkowski, Test examples for nonlinear programming codes, Report, Institut für Informatik, Universität Stuttgart, FRG (1984).

    Google Scholar 

  31. R.B. Wilson, A simplicial algorithm for concave programming, Ph.D. Thesis, Graduate School of Business Administration, Harvard University, Boston (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Schittkowski, K. NLPQL: A fortran subroutine solving constrained nonlinear programming problems. Ann Oper Res 5, 485–500 (1986). https://doi.org/10.1007/BF02022087

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02022087

Keywords and phrases

  • Nonlinear programming
  • sequential quadratic programming method
  • numerical implementation
  • test results