Skip to main content
SpringerLink
Log in

Discrete solutions to engineering design problems

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Summary

A method of obtaining discrete and/or integer valued solutions to non-linear design problems is presented. The general framework is that of geometric programming which is combined with the Branch and Bound Method. Recently developed computational procedures are described and are used to demonstrate the feasibility of the above method.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Avriel and D. J. Wilde, Optimal Condenser Design by Geometric Programming,Ind. Eng. Chem. Process Design and Dev., 6 (1967) 256–263.

    Google Scholar 

  2. M. Avriel and A. C. Williams, Complementary Geometric Programming,SIAM J. Appl. Math., 19 (1970) 125–141.

    Google Scholar 

  3. M. Avriel and A. C. Williams, An Extension of Geometric Programming with Applications in Engineering Optimization,J. of Eng. Math., 5 (1971) 187–194.

    Google Scholar 

  4. E. Balas, A Note on the Branch and Bound Principle,Oprs. Res., 16 (1968) 442–445.

    Google Scholar 

  5. S. G. Beveridge and R. S. Schechter,Optimization: Theory and Practice, McGraw-Hill, New York (1970).

    Google Scholar 

  6. R. Dembo, M. Avriel and U. Passy,An Algorithm for the Solution of Generalized Geometric Programs, paper presented at XIX TIMS, Houston, Texas, April 1972.

  7. J. J. Dinkel, W. H. Elliott and G. A. Kochenberger,A Linear Programming Approach to Geometric Programs, submitted for publication.

  8. R. J. Duffin, Linearizing Geometric Programs,SIAM Review, 12 (1970) 211–237.

    Google Scholar 

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

    Google Scholar 

  10. J. E. Falk,Global Solutions of Signomial Programs, Report T-274, Institute for Management Science and Engineering, The George Washington University, June (1973).

  11. J. E. Falk and R. M. Soland, An Algorithm for Separable Non-Convex Programming Problems,Management Science, 15 (1969) 550–569.

    Google Scholar 

  12. F. S. Hillier and G. J. Leiberman,Introduction to Operations Research, Holden-Day (1967).

  13. J. E. Kelley, The Cutting Plane Method for Solving Convex Programs,SIAM J. Appl. Math., 8 (1960) 703–712.

    Google Scholar 

  14. L. G. Mitten, Branch and Bound Methods: General Formulation and Properties,Opers. Res., 18 (1970) 24–34.

    Google Scholar 

  15. R. M. Stark and R. L. Nicholls,Mathematical Foundations for Design, Civil Engineering Systems, McGraw-Hill (1972).

  16. D. J. Wilde and C. S. Beightler,Foundations of Optimization, Prentice-Hall, Englewood Cliffs (1967).

    Google Scholar 

  17. W. I. Zangwill,Nonlinear Programming, Prentice-Hall (1969).

Download references

Author information

Authors and Affiliations

  1. Department of Management Science and Organizational Behavior, The Pennsylvania State University, 16802, University Park, Pennsylvania, USA

    J. J. Dinkel & G. A. Kochenberger

Authors
  1. J. J. Dinkel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. A. Kochenberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dinkel, J.J., Kochenberger, G.A. Discrete solutions to engineering design problems. J Eng Math 9, 29–38 (1975). https://doi.org/10.1007/BF01535495

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01535495

Keywords

Search

Navigation