Nonsmooth maximum principle for infinite-horizon problems

  • J. J. Ye
Contributed Papers


In this paper, we consider a class of infinite-horizon discounted optimal control problems with nonsmooth problem data. A maximum principle in terms of differential inclusions with a Michel type transversality condition is given. It is shown that, when the discount rate is sufficiently large, the problem admits normal multipliers and a strong transversality condition holds. A relationship between dynamic programming and the maximum principle is also given.

Key Words

Infinite-horizon problems optimal control transversality condition maximum principle nonsmooth analysis 


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  1. 1.
    Halkin, H.,Necessary Conditions for Optimal Control Problems with Infinite Horizons, Econometrica, Vol. 42, pp. 267–272, 1974.Google Scholar
  2. 2.
    Aubin, J. P., andClarke, F. H.,Shadow Prices and Duality for a Class of Optimal Control Problems, SIAM Journal on Control and Optimization, Vol. 17, pp. 567–586, 1979.Google Scholar
  3. 3.
    Michel, P.,On the Transversality Condition in the Infinite-Horizon Optimal Problems, Econometrica, Vol. 50, pp. 975–985, 1982.Google Scholar
  4. 4.
    Clarke, F. H.,Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, New York, 1983.Google Scholar
  5. 5.
    Ye, J. J.,Optimal Control of Piecewise Deterministic Markov Processes, PhD Thesis, Dalhousie University, 1990.Google Scholar
  6. 6.
    Carlson, D. A., andHaurie, A.,Infinite-Horizon Optimal Control, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, Germany, Vol. 290, 1987.Google Scholar
  7. 7.
    Clarke, F. H., andVinter, R. B.,The Relationship between the Maximum Principle and Dynamic Programming, SIAM Journal on Control and Optimization, Vol. 25, pp. 1291–1311, 1987.Google Scholar
  8. 8.
    Vinter, R. B.,New Results on the Relationship between Dynamic Programming and the Maximum Principle, Mathematics of Control, Signals, and Systems, Vol. 1, pp. 97–105, 1988.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • J. J. Ye
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of VictoriaBritish ColumbiaCanada

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