Abstract
This paper tries to make three steps towards more efficient applicability of mathematical programming algorithms : First, a program package is presented which easily allows comparisons of different algorithms applied to a specific minimization problem. All the algorithms use similar, problem-dependent termination criteria. Secondly, an efficient standard algorithm for unconstrained optimization without using derivatives is described. It is a quasi-Newton method in which the termination criterion of the unidimensional searches becomes refined according to the convergence of the multidimensional optimization. The required gradients are evaluated by numerical differences using step-lengths which iteratively are optimized to get maximum accuracy. Thirdly, the user of the nonlinear programming package has the option to leave the selection of the optimization method up to the program. Numerical examples are presented.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
L.C.W. Dixon: Optimization in Action. Academic Press, London, 1976.
S.L. Jacoby, J.S. Kowalik, J.T. Pizzo: Iterative Methods for Nonlinear Optimization Problems. Prentice-Hall, 1972.
D. Rufer: Mathematische Programmierung — eine Uebersicht. Angewandte Informatik, 3, 1974.
D. Rufer: Optimale Steuerung des Zweikörperproblems. Dissertation No.5519, Eidgenössische Technische Hochschule Zürich, 1975.
H.J. Kelley, W.F. Denham, I.L. Johnson, P.O. Wheatley: An Accelerated Gradient Method for Parameter Optimization with Nonlinear Constraints. Journal of the Astronautical Sciences, Vol XIII, No 4, 1966.
I.L. Johnson: The Davidon-Fletcher-Powell Penalty Function Method — a Generalized Iterative Technique for Solving Parameter Optimization Problems. Johnson Space Center, Internal Note No 75-FM-34, Houston 1975.
R. Fletcher, M. Powell: A Rapidly Convergent Descent Method for Minimization. Computer Journal, Vol 6, 1963.
J.D. Pearson: Variable Metric Methods of Minimization. Computer Journal, Vol 12, 1969.
R. Fletcher: A New Approach to Variable Metric Algorithms. Computer Journal, Vol 13, 1970.
G. Guilfoyle, I. Johnson, P. Wheatley: One-dimensional Search Combining Golden Section and Cubic Fit Techniques. NASA CR-65994, 1967.
G.W. Stewart: A Modification of Davidon's Minimization Method to Accept Difference Approximations of Derivatives. Journal of ACM, Vol 14, 1967.
D. Rufer: Implementation and Properties of a Method for the Identification of Nonlinear Continuous Time Models. Bericht Nr. 77-01, Fachgruppe für Automatik, Eidgenössische Technische Hochschule, Zürich, 1977.
H. Mäder, P. Wehrli: Modelling of a Reservoir. Proceedings of the IFIP Working Conference on Modeling and Simulation of Land, Air, Water Ressources Systems, Ghent, Belgium, August 1977.
J. Leimgruber; Stationary and Dynamic Behaviour of a Speed Controlled Synchronous Motor with cosϕ — or Commutation Limit Line Control. IFAC Symposium on Control in Power Electronics and Electrical Drives, Düsseldorf, Oct. 3–5, 1977.
D. Rufer: Trajectory Optimization by Making Use of the Closed Solution of Constant Thrust-Acceleration Motion. Celestial Mechanics, Vol 14, 1976.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this paper
Cite this paper
Rufer, D.F. (1978). General purpose nonlinear programming package. In: Stoer, J. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006555
Download citation
DOI: https://doi.org/10.1007/BFb0006555
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08708-3
Online ISBN: 978-3-540-35890-9
eBook Packages: Springer Book Archive