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.
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References
J. Abadie, Méthode du gradient réduit generalisé: Le code GRGA, Note HI 1756/00, Electricite de France, Paris (1975).
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.
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).
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).
A.V. Fiacco and G.P. McCormick,Nonlinear Sequential Unconstrained Minimization Techniques (Wiley, New York, 1968).
R. Fletcher, A FORTRAN program for general quadratic programming, Report No. R6370, AERE, Harwell, Berkshire (1970).
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).
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.
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).
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).
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).
S.-P. Han, Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Mathematical Programming 11(1976)263.
S.-P. Han, A globally convergent method for nonlinear programming, J. of Optimization Theory and Applications 22(1977)297.
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).
W. Hock and K. Schittkowski, A comparative performance evaluation of 27 nonlinear programming codes, Computing 30(1983)335.
W. Kribbe, Documentation of the FORTRAN-subroutines for quadratic programming CONQUA and START, Report 8231/1, Econometric Institute, Erasmus University, Rotterdam (1982).
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).
C.L. Lawson and R.J. Hanson,Solving Least Squares Problems (Prentice Hall, Englewood Cliffs, New Jersey, 1974).
D.A. Pierre and M.J. Lowe,Mathematical Programming via Augmented Lagrangians (Addison-Wesley, Reading, Massachusetts, 1975).
M.J.D. Powell, A fast algorithm for nonlinearly constrained optimization calculations, in:Numerical Analysis, ed. G.A. Watson,Lecture Notes in Mathematics, Vol. 630 (Springer-Verlag, Berlin-Heidelberg-New York, 1978).
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).
M.J.D. Powell, VMCWD: A FORTRAN subroutine for constrained optimization, Report DAMTP 1982/NA4, University of Cambridge, Cambridge (1982).
M.J.D. Powell, ZQPCVX: A FORTRAN subroutine for convex quadratic programming, Report DAMTP 1983/NA17, University of Cambridge, Cambridge (1983).
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).
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).
K. Schittkowski,Nonlinear Programming Codes, Lecture Notes in Economics and Mathematical Systems, Vol. 183 (Springer-Verlag, Berlin-Heidelberg-New York, 1980).
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.
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.
K. Schittkowski, User’s guide for the nonlinear programming code NLPQL, Report, Institut für Informatik, Universität Stuttgart, FRG (1984).
K. Schittkowski, Test examples for nonlinear programming codes, Report, Institut für Informatik, Universität Stuttgart, FRG (1984).
R.B. Wilson, A simplicial algorithm for concave programming, Ph.D. Thesis, Graduate School of Business Administration, Harvard University, Boston (1963).
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Schittkowski, K. NLPQL: A fortran subroutine solving constrained nonlinear programming problems. Ann Oper Res 5, 485–500 (1986). https://doi.org/10.1007/BF02739235
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DOI: https://doi.org/10.1007/BF02739235