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First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function

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Abstract

The paper deals with a nonlinear discrete-time optimal control problem with a vector-valued objective function of terminal type. For the admissible controls of the problem under consideration which satisfy the additional regularity condition of the Lyusternik type we prove the first and second necessary optimality conditions extending such the classical optimality conditions as the Euler condition and the negativity of second variation of the objective function.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, Belarus

    Valentin V. Gorokhovik

  2. Department of Mathematics, Belarusian State Economic University, Minsk, Belarus

    Svetlana Ya. Gorokhovik

  3. Faculty of Mining and Geology, University of Belgrade, Belgrade, Serbia

    Boban Marinković

Authors
  1. Valentin V. Gorokhovik
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  2. Svetlana Ya. Gorokhovik
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  3. Boban Marinković
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Correspondence to Valentin V. Gorokhovik.

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Gorokhovik, V.V., Gorokhovik, S.Y. & Marinković, B. First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function. Positivity 17, 483–500 (2013). https://doi.org/10.1007/s11117-012-0183-7

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  • DOI: https://doi.org/10.1007/s11117-012-0183-7

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