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First and second order sufficient conditions for optimal control and the calculus of variations

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Abstract

In this paper we develop first and second order sufficient conditions for optimal control and the calculus of variations problems. Our conditions are derived from the Hamilton-Jacobi approach [15, Thm. 2], which was obtained for the generalized problem of Bolza. We do not require any convexity on the data [7] and [11], or that the control setU is polyhedral [14], or that the control function is in the interior ofU [8]. Instead, we assume a certain inequality which is satisfied in each of the above mentioned cases.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

    Vera Zeidan

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  1. Vera Zeidan
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Communicated by A. V. Balakrishnan

The publication of this report has been made possible due to a grant of the Fonds FCAC for the help and support of research.

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Zeidan, V. First and second order sufficient conditions for optimal control and the calculus of variations. Appl Math Optim 11, 209–226 (1984). https://doi.org/10.1007/BF01442179

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