Skip to main content
Log in

Linearly constrained optimization

Optimierung mit linearen Restriktionen

  • Short Communications
  • Published:
Computing Aims and scope Submit manuscript

Abstract

For linearly constrained optimization problems an algorithm is presented which is based on conjugate gradients. Numerical tests demonstrate a favourable behaviour of the new algorithm.

Zusammenfassung

Zur Lösung von Optimierungsproblemen mit linearen Restriktionen wird ein Algorithmus auf der Grundlage konjugierter Gradienten vorgestellt. Einige Testbeispiele zeigen hervorragendes Konvergenzverhalten.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Best, M. J., Ritter, K.: An accelerated conjugate direction method to solve linearly constrained minimization problems. Journal of Comp. and System. Sciences11, 295–322 (1975).

    Google Scholar 

  2. Gill, P. E. et al.: Methods for modifying matrix factorization. Mathematics of Computations28, 505–535 (1974).

    Google Scholar 

  3. Gill, P. E., Murray, W., Wright, M. H.: Practical Optimization. London: Academic Press 1981.

    Google Scholar 

  4. Goldfarb, D.: Extension of Davidson's variable metric method to maximization under linearly inequality and equality constraints. SIAM J. Appl. Math.17, 739–763 (1969).

    Google Scholar 

  5. Hestens, M.: Conjugate Direction Methods in Optimization. New York-Heidelberg-Berlin: Springer-Verlag 1980.

    Google Scholar 

  6. Himmelblau, D.: Applied Nonlinear Programming. New York: McGraw-Hill 1972.

    Google Scholar 

  7. Hock, W., Schitkowski, K.: Test Examples for Nonlinear Codes. Lecture Notes in Economics and Mathematical Systems. Berlin-Heidelberg-New York: Springer-Verlag 1981.

    Google Scholar 

  8. Lasdon, L. S., et al.: Design and testing of generalized reduced gradient for nonlinear programming. ACM Transaction on Math. Software4, 34–50 (1978).

    Google Scholar 

  9. Murtagh, A., Saunders, M.: A projected lagrangian algorithm and its implementation for sparse nonlinear constraints. Mathem. Program. Study16, 84–117 (1982).

    Google Scholar 

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

    Google Scholar 

  11. Strang G.: Linear Algebra and its Applications. New York: Academic Press 1976.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ostrovsky, G.M., Ostrovsky, M.G. & Berezinsky, T.A. Linearly constrained optimization. Computing 42, 85–89 (1989). https://doi.org/10.1007/BF02243146

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02243146

AMS Subject Classifications

Key words

Navigation