Skip to main content
Log in

An approach to the numerical solutions of geometric programs

  • Published:
Mathematical Programming Submit manuscript

Abstract

An algorithm for solving ordinary geometric programs is presented. The algorithm is based on the reduced system associated with geometric programs and is highly flexible in that it allows the use of several nonlinear optimization techniques.

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.

Similar content being viewed by others

References

  1. P. Beck, “A modified convex simplex algorithm for geometric programming with subsidiary problems”, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N.Y. (1972).

    Google Scholar 

  2. P. Beck and J.G. Ecker, “Some computational experience with a modified convex simplex algorithm for geometric programming”,Journal of Optimization Theory and Applications 14 (6) 1974.

  3. R. Bellman,Introduction to matrix analysis (McGraw-Hill, New York, 1970).

    Google Scholar 

  4. R.J. Clasen, “The numerical solution of the chemical equilibrium problem”, The RAND Corporation, RM-4345 (1965).

  5. J. Dinkel and G.A. Kochenberger, “On geometric programming and the chemical equilibrium problem”, paper presented at XIX TIMS Meeting, Houston, April 1972.

  6. R.J. Duffin, E.L. Peterson and C. Zener,Geometric programming (Wiley, New York, 1967).

    Google Scholar 

  7. C.J. Frank, “An algorithm for geometric programming”, in:Recent advances in optimization techniques, Eds. A. Lavi and T. Vogl (Wiley, New York, 1965) pp. 145–162.

    Google Scholar 

  8. R. Hooke and T.A. Jeeves, “Direct search solution of numerical and statistical problems”,Journal of the Association for Computing Machinery 8 (2) (1961) 212.

    Google Scholar 

  9. H.P. Kunzi, W. Krelle and W. Oettli,Nonlinear programming (Blaisdell, Waltham, Mass., 1966).

    Google Scholar 

  10. E. Polak,Computational methods in optimization (Academic Press, New York, 1971).

    Google Scholar 

  11. A.C. Williams, private communication.

  12. R.M. Dembo, M. Avriel and U. Passy, “An algorithm for the solution of generalized geometric programs”, paper presented at 41st TIMS, Houston, Texas, 1972.

  13. J.J. Dinkel, G.A. Kochenberger and B. McCarl, “A computational study of methods for solving polynomial geometric programs”,Journal of Optimization Theory and Applications, to appear.

  14. R. Fletcher, “An algorithm for solving linearly constrained optimization problems”,Mathematical Programming 2 (1972) 133–165.

    Google Scholar 

  15. T. Jefferson, “Geometric programming with an application to transport planning”, Ph.D. Thesis, Northwestern University, Evanston, Ill. (1972).

    Google Scholar 

  16. G.A. Kochenberger, R.E.D. Woolsey and B. McCarl, “On the solution of geometric programs via separable programming”,Operational Research Quarterly 24 (1973) 285–294.

    Google Scholar 

  17. A.B. Templeman, A. Wilson and K. Winterbottom, “SIGNOPT — A computer code for signomial geometric programming”, Department of Civil Engineering, University of Liverpool (1972).

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dinkel, J.J., Kochenberger, G.A. & McCarl, B. An approach to the numerical solutions of geometric programs. Mathematical Programming 7, 181–190 (1974). https://doi.org/10.1007/BF01585514

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01585514

Keywords

Navigation