Abstract
Automated heuristic reasoning plays a more and more important role in mathematical programming, since more and more application problems, algorithms and codes are available and in the hands of unexperienced or occasional users. The decision, how to model the problem, how to select a suitable code or how to interpret results and failure messages, is still a nontrivial task even for well-experienced specialists. The paper presents some ideas and investigations how to implement the heuristic knowledge of experts by means of suitable software tools. To illustrate the approach in more detail, an interactive programming system for mathematical programming is described which is capable to evaluate some of the heuristics mentioned above.
Preview
Unable to display preview. Download preview PDF.
References
Brown, K.M., Dennis, J.E. (1972): Derivative free analogues of the Levenberg-Marquardt and Gauss-Newton algorithms for nonlinear least squares approximations, Numerische Mathematik, Vol. 18, 289–297.
Dennis, Jr., D.M., Gay, D.M., Welsch (1981a): An adaptive nonlinear least-squares algorithm, ACM Transactions on Mathematical Software, Vol. 7, 348–368.
Dennis, Jr., D.M., Gay, D.M., Welsch (1981b): Algorithm 573. NL2SOL — An adaptive nonlinear least-squares algorithm, ACM Transactions on Mathematical Software, Vol. 7, 369–383.
Ecker, J.G., Kupferschmid, M. (1983): An ellipsoid algorithm for nonlinear programming, Mathematical Programming, Vol. 27, 83–106.
Goldfarb, D., Idnani, A. (1983): A numerically stable dual method for solving strictly convex quadratic programs, Mathematical Programming, Vol. 27, 1–33.
Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H. (1983a): User's guide for SOL/NPSOL: a FORTRAN package for nonlinear programming, Report SOL 83-12, Department of Operations Research, Stanford University, USA.
Gill, P.E., Murray, W., Saunders, M.A., Wright, M.H. (1983b): User's guide for SOL/QPSOL: a FORTRAN package for quadratic programming, Report SOL 83-7, Department of Operations Research, Stanford University, USA.
Han, S.-P. (1976): Superlinearly convergent variable metric algorithms for general nonlinear programming problems, Mathematical Programming, Vol. 11, 263–282.
Han, S.-P. (1977): A globally convergent method for nonlinear programming, Journal of Optimization Theory and Applications, Vol. 22, 297–309.
Lemarechal, C., Strodiot, J.-J., Bihain, A. (1981): On a bundle algorithm for nonsmooth optimization, in: Mangasarian, O.L., Meyer, R.R., Robinson, S.M.: Nonlinear programming, Academic Press.
Lindstroem, P. (1983): Algorithms for nonlinear least squares particularly problems with constraints, Report UMINF-106.83, Institute of Information Processing, University of Umea, Sweden.
Powell, M.J.D. (1978a): A fast algorithm for nonlinearly constrained optimization calculations, in: Numerical Analysis, G.A. Watson ed., Lecture Notes in Mathematics, Vol. 630, Springer, Berlin, Heidelberg, New York.
Powell, M.J.D. (1978b): The convergence of variable metric methods for nonlinearly constrained optimization calculations, in: Nonlinear Programming 3, O.L. Mangasarian, R.R Meyer, S.M. Robinson eds., Academic Press, New York, San Francisco, London.
Powell, M.J.D. (1983): On the quadratic programming algorithm of Goldfarb and Idnani, Report DAMTP 1983/Na 19, University of Cambridge, Cambridge, Great Britain.
Schittkowski, K. (1983): On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function, Mathematische Operationsforschung und Statistik, Series Optimization, Vol. 14, 197–216.
Schittkowski, K. (1985): Solving constrained nonlinear least squares problems by a general purpose SQP-method, in: Trends in Mathematical Optimization, K.-H. Hoffmann, J.-B. Hiriart-Urruty, C. Lemarechal, J. Zowe eds., International Series of Numerical Mathematics, Vol. 84, Birkhaeuser, Basel, Boston, 1988.
Schittkowski, K. (1985/86): NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems, Annals of Operations Research, Vol. 5, 485–500.
Schittkowski, K. (1986a): ELL: A FORTRAN implementation of an ellipsoid algorithm for nonlinear programming, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1986b): MCO: A FORTRAN implementation of an interactive multicriterion optimization method, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1986c): DFNLP: A FORTRAN implementation of an SQP-algorithm for constrained nonlinear data fitting and min-max problems, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1986d): DFELL: A FORTRAN implementation of an ellipsoid algorithm for nonlinear data fitting, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1986e): QL: A FORTRAN implementation of a dual algorithm for quadratic programming, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1986f): LP: A FORTRAN implementation of the simplex algorithm for linear programming, User's Guide, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1987): Die Systementwicklungssprache SUSY, Report, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schittkowski, K. (1989): An SQP-method for solving nonlinear programming problems with very many constraints, Report, Mathematisches Institut, Universitaet Bayreuth, 8580 Bayreuth.
Schramm, H. (1989): Eine Kombination von Bundle-und Trust-Region-Verfahren zur Loesung nichtdifferenzierbarer optimierungsprobleme, Dissertation, Mathematisches Institut, Universitaet Bayreuth.
Shor, N.Z. (1977): Cut-off method with space extension in convex programming problems, Cybernetics, Vol. 12, 94–96.
Torn, A., Zilinskas, A. (1989): Global Optimization, Lecture Notes in Computer Science, Vol. 350, Springer, Berlin, Heidelberg, New York.
Wilson, R.B. (1963): A simplicial algorithm for concave programming, Ph.D. Thesis, Graduate School of Business Administration, Harward University, Boston, USA.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 International Federation for Information Processing
About this paper
Cite this paper
Schittkowski, K. (1990). Heuristic reasoning in mathematical programming. In: Sebastian, H.J., Tammer, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008451
Download citation
DOI: https://doi.org/10.1007/BFb0008451
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52659-9
Online ISBN: 978-3-540-47095-3
eBook Packages: Springer Book Archive