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Necessary Conditions in Mathematical Programming and Optimal Control Theory

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Optimal Control Theory and its Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((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.

This paper is the write-up of a series of lectures given at the 14th Biennial Seminar of the Canadian Mathematical Congress. This paper was written while the author was a visiting member of the Centre de Recherches Mathématiques at the Université de Montréal.

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References

  1. Carathéodory, C., Calculus of Variations and Partial Differ- ential Equations of the First Order, Holden-Day, San Francisco, 1967.

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  2. Halkin, H., On the necessary condition for optimal control of nonlinear systems, J. An. Math., 12, 1964, pp. 1–82.

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  3. 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, 1968

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  4. 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.

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  5. McShane, E. J., On Multipliers for Lagrange Problems, Amer. J. Math., 61, 1939, pp. 809–819.

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  6. Pontryagin, L. S., and The mathematical theory of optimal processes, Wiley, New York, 1962.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Dan Diego, USA

    Hubert Halkin

Authors
  1. Hubert Halkin
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Editor information

Editors and Affiliations

  1. Mathematics Department, Queen’s University, Kingston, Ontario, Canada

    Bruce J. Kirby

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© 1974 Springer-Verlag Berlin Heidelberg

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Halkin, H. (1974). Necessary Conditions in Mathematical Programming and Optimal Control Theory. In: Kirby, B.J. (eds) Optimal Control Theory and its Applications. Lecture Notes in Economics and Mathematical Systems, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01569-8_2

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  • DOI: https://doi.org/10.1007/978-3-662-01569-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07018-4

  • Online ISBN: 978-3-662-01569-8

  • eBook Packages: Springer Book Archive

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