A new sufficient condition for most rapid approach paths

  • R. F. Hartl
  • G. Feichtinger
Technical Note


In this paper, we show that in some previous literature the most rapid approach theorems are incomplete. This is proved by providing a counterexample. We also introduce an additional condition that guarantees the optimality of the most rapid approach path.

Key Words

Optimal control Green's theorem method infinite-horizon problems most rapid approach 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Miele, A.,Extremization of Linear Integrals by Green's Theorem, Optimization Techniques, Edited by G. Leitmann, Academic Press, New York, New York, pp. 69–98, 1962.Google Scholar
  2. 2.
    Spence, M., andStarrett, D.,Most Rapid Approach Paths in Accumulation Problems, International Economic Review, Vol. 16, pp. 388–403, 1975.Google Scholar
  3. 3.
    Sethi, S. P.,Nearest Feasible Paths in Optimal Control Problems: Theory, Examples, and Counterexamples, Journal of Optimization Theory and Applications, Vol. 23, pp. 563–579, 1977.Google Scholar
  4. 4.
    Sethi, S. P., andThompson, G. L.,Optimal Control Theory: Applications to Management Science, Martinus Nijhoff, Boston, Massachusetts, 1981.Google Scholar
  5. 5.
    Feichtinger, G., andHartl, R. F.,Optimale Kontrolle Ökonomischer Prozesse: Anwendungen des Maximumprinzips in den Wirtschaftswissenschaften, De Gruyter, Berlin, West Germany, 1986.Google Scholar
  6. 6.
    Arrow, K. J.,Optimal Capital Policy, the Cost of Capital, and Myopic Decision Rules, Annals of the Institute of Statistical Mathematics, Vol. 16, pp. 21–30, 1964.Google Scholar
  7. 7.
    Clark, C. W.,Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Wiley, New York, New York, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • R. F. Hartl
    • 1
  • G. Feichtinger
    • 1
  1. 1.Institute for Econometrics and Operations ResearchUniversity of TechnologyViennaAustria

Personalised recommendations