Skip to main content
SpringerLink
Log in

A note on the free terminal time transversality condition

  • Papers
  • Series A: Theory
  • Published:
Zeitschrift für Operations-Research Aims and scope Submit manuscript

Abstract

This note clarifies some issues dealing with the necessary condition for the optimal terminal time in free terminal time optimal control problems. It is shown that this condition is independent of the other maximum principle conditions and a simple proof is presented. Also the economic interpretation of the condition is provided.

Zusammenfassung

In dieser Arbeit werden einige Fragen im Zusammenhang mit der Bestimmung des optimalen Endzeitpunktes bei optimalen Kontrollproblemen geklärt. Ein einfacher Beweis der entsprechenden notwendigen Optimalitätsbedingung zeigt, daß diese Bedingung unabhängig von den übrigen Aussagen des Pontrjaginschen Maximumprinzips ist. Weiters wird eine ökonomische Interpretation dieser Bedingung präsentiert.

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

  • Arora, S.R., andP. T. Lele: A Note on Optimal Maintenance Policy and Sale Date of a Machine, Management Science17 (3), 1970, 170–173.

    Article  MATH  Google Scholar 

  • Athans, M., andP.L. Falb: Optimal Control: An Introduction to the Theory and its Applications. New York 1966.

  • Bensoussan, A., E.G. Hurst, andB. Näslund: Management Applications of Modern Control Theory. Amsterdam 1974.

  • Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources. New York 1976.

  • Hestenes, M.R.: On Variational Theory and Optimal Control Theory. J. SIAM Control3 (1), 1965, 23–48.

    MathSciNet  MATH  Google Scholar 

  • Kamien, M.I., andN.L. Schwartz: Optimal Maintenance and Sale Age for a Machine Subject to Failure. Management Science17 (8), 1971, 495–504.

    Article  MathSciNet  MATH  Google Scholar 

  • Lee, E.B., andL. Markus: Foundations of Optimal Control Theory. New York 1967.

  • Näslund, B.: Simultaneous Determination of Optimal Repair Policy and Service Life. The Swedish Journal of Economics68, 1966, 64–73.

    Google Scholar 

  • —: Optimal Rotation and Thinning. Forest Science15, 1969, 446–451.

    Google Scholar 

  • Pierskalla, W.P., andJ.A. Voelker: A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems. Naval Research Logistics Quarterly23, 1976, 353–388.

    Article  MathSciNet  MATH  Google Scholar 

  • Pontryagin, L.S., et al.: The Mathematical Theory of Optimal Processes. New York 1962.

  • Rapp, B.: Models for Optimal Investment and Maintenance Decisions. Stockholm 1974.

  • Sadowski, D.: Optimale Pensionierungsentscheidungen, Angewandte Planung2, 1978, 122–130.

    Google Scholar 

  • Sethi, S.P.: An Application of Optimal Control Theory in Forest Management. Journal of Management Science and Applied Cybernetics2, 1973a, 9–16.

    MATH  Google Scholar 

  • —: Simultaneous Optimization of Preventive Maintenance and Replacement Policy for Machines: A Modern Control Theory Approach AIIE Transactions5 (2), 1973b, 156–163.

    MathSciNet  Google Scholar 

  • Sethi, S.P., andG.L. Thompson: Optimal Control Theory: Applications to Management Science. Boston 1981.

  • Tapiero, C.S., andI. Venezia: A Mean Variance Approach to the Optimal Machine Maintenance and Replacement Problem. Journal of the Operational Research Society30 (5), 1979, 457–466.

    Article  MathSciNet  MATH  Google Scholar 

  • Thompson, G.L.: Optimal Maintenance Policy and Sale Date of a Machine. Management Science14 (9), 1968, 543–550.

    Article  Google Scholar 

  • Vincent, T.L., andR.G. Brusch: Optimal Endpoints, Journal of Optimization Theory and Applications6 (4), 1970.

  • Vincent, T.L., andB.S. Goh: Terminality, Normality and Transversality Conditions. Journal of Optimization Theory and Applications9 (1), 1972.

Download references

Author information

Authors and Affiliations

  1. Institut für ökonometrie und Operations Research, Technische Universität Wien, Argentinierstr. 8, A-1040, Wien

    R. F. Hartl

  2. Faculty of Management Studies, University of Toronto, 246 Bloor Street West, M5S 1V4, Toronto, Ontario, Canada

    S. P. Sethi (Professor)

Authors
  1. R. F. Hartl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. P. Sethi
    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

Hartl, R.F., Sethi, S.P. A note on the free terminal time transversality condition. Zeitschrift für Operations Research 27, 203–208 (1983). https://doi.org/10.1007/BF01916915

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01916915

Keywords

Search

Navigation