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Necessary Conditions in Mathematical Programming and Optimal Control Theory

  • Hubert Halkin
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 105)

Abstract

In these lectures I will present a theory of necessary conditions for nonlinear optimizations problems in infinite-dimensional spaces and I will apply the results of the theory to the optimal control of systems described by families of nonlinear ordinary differential equations.

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References

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    Carathéodory, C., Calculus of Variations and Partial Differ- ential Equations of the First Order, Holden-Day, San Francisco, 1967.Google Scholar
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    Halkin, H., On the necessary condition for optimal control of nonlinear systems, J. An. Math., 12, 1964, pp. 1–82.MathSciNetMATHCrossRefGoogle Scholar
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    Halkin, H., Nonlinear nonconvex programming in an infinite dimensional space, in “Mathematical Theory of Control”, A. V. Balakrishnan and L. W. Neustadt, eds., Academic Press, 1968Google Scholar
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    John, F., Extremum Problems with Inequalities as Subsidiary Conditions, in K. O. Friedricks, O. E. Neugebauer, and J. J. Stoker, (eds.) “Studies and Essays: Courant Anniversary Volume”, pp. 187–204, Interscience Publishers, New York, 1948.Google Scholar
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    McShane, E. J., On Multipliers for Lagrange Problems, Amer. J. Math., 61, 1939, pp. 809–819.MathSciNetCrossRefGoogle Scholar
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    Pontryagin, L. S., and The mathematical theory of optimal processes, Wiley, New York, 1962.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Hubert Halkin
    • 1
  1. 1.Department of MathematicsUniversity of California at Dan DiegoUSA

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