Skip to main content

Advertisement

SpringerLink
Log in

Case Studies in Optimization: Catenary Problem

  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

This is the second paper in a series presenting case studies in modern large-scale constrained optimization 9 In this paper, we consider the shape of a hanging chain, which, in equilibrium, minimizes the potential energy of the chain. In addition to the tutorial aspects of this paper, we also emphasize the importance of certain modeling issues such as convex vs. nonconvex formulations of given problem. We will present several models of the problem and demonstrate differences in the number of iterations and solution time.

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

  • N. I. Akhiezer, The Calculus of Variations, Blaisdell Pub. Co., New York, 1962.

    Google Scholar 

  • I. M. Gelfand and S. V. Fomin, Calculus of Variations, Prentice-Hall, Inc, Englewood Cliffs, NJ, 1963.

    Google Scholar 

  • A. S. Bondarenko, D. M. Bortz, and J. J. More, COPS: Constrained Optimization Problems, Mathematics and Computer Science Division, Argonne National Laboratory, http://www-unix.mcs.anl.gov/more/cops

  • A. S. Bondarenko, D. M. Bortz, and J. J. More, “COPS: Large-scale Nonlinearly Constrained Optimization Problems,” Mathematics and Computer Science Division, Argonne National Laboratory, Technical Report ANL/MCS-TM-237, 1999.

  • R. Fourer, D. M. Gay, and B. W. Kernigan, AMPL: A modeling Language for Mathematical Programming, Scientific Press, 1993.

  • R. J. Vanderbei and D. F. Shanno, “An interior-point algorithm for nonconvex nonlinear programming,” COAP vol. 13, pp. 231–252, 1999.

    Google Scholar 

  • R. J. Vanderbei, “LOQO: An interior point code for quadratic programming,” Optimization Methods and Software, vol. 12, pp. 451–484, 1999a.

    MathSciNet  Google Scholar 

  • R. J. Vanderbei, “LOQO user’s manual—version 3.10,” Optimization Methods and Software, vol. 12, pp. 485–514, 1999b.

    MathSciNet  Google Scholar 

  • R. J. Vanderbei, “Case Studies in Trajectory Optimization: Trains, Planes, and Other Pastimes,” Optimization and Engineering, vol. 2, pp. 215–243, 2001.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Operations Research and Financial Engineering, Princeton University, USA

    Igor A. Griva & Robert J. Vanderbei

Authors
  1. Igor A. Griva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert J. Vanderbei
    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

Griva, I.A., Vanderbei, R.J. Case Studies in Optimization: Catenary Problem. Optim Eng 6, 463–482 (2005). https://doi.org/10.1007/s11081-005-2068-0

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-005-2068-0

Keywords

Search

Navigation