Skip to main content
Log in

A set of geometric programming test problems and their solutions

  • Published:
Mathematical Programming Submit manuscript

Abstract

This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.

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. M. Avriel and A.C. Williams, “An extension of geometric programming with applications in engineering optimization”,Journal of Engineering Mathematics 5 (3) (1971) 187–194.

    Article  Google Scholar 

  2. P.A. Beck and J.G. Ecker, “A modified concave simplex algorithm for geometric programming”,Journal of Optimization Theory and Applications, to appear.

  3. J. Bracken and G.P. McCormick, “Selected applications in nonlinear programming” (Wiley, New York, 1968) pp. 37–45.

    MATH  Google Scholar 

  4. A.R. Colville, “A comparative study of nonlinear programming codes”, IBM NYSC Rept. 320-2949 (1968).

  5. G.B. Dantzig, J.C. de Haven and C.P. Sams, in:Proceedings of the 4th Berkeley symposium on mathematical statistics and probability (University of California Press, Berkeley, Calif., 1960) pp. 181–196.

    Google Scholar 

  6. R.S. Dembo, “Solution of complementary geometric programming problems”, M.Sc. Thesis, Technion, Haifa (1972).

    Google Scholar 

  7. R.S. Dembo, “GGP — A program for solving generalized geometric programs — Users Manual”, Department of Chemical Engineering Rept. 72/59, Technion (1972).

  8. R.S. Dembo, M. Avriel and U. Passy, “An algorithm for the solution of generalized geometric programs”,International Journal for Numerical Methods in Engineering, to appear.

  9. J. Haldi, “25 integer programming test problems”, Stanford University, Graduate School of Business, Working Paper no. 43 (December 1964).

  10. M.J. Rijckaert, “Engineering applications of geometric programming”, in: M. Avriel, M.J. Rijckaert and D.J. Wilde, eds.,Optimization and design (Prentice Hall, Englewood Cliffs, N.J., 1973) pp. 196–220.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported in part by Canada Council Grant #S74-0148 and National Research Council of Canada Grant #084-6319-32.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dembo, R.S. A set of geometric programming test problems and their solutions. Mathematical Programming 10, 192–213 (1976). https://doi.org/10.1007/BF01580667

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01580667

Keywords

Navigation