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Existence of optimal controls with discrete decisions

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  • Dean A. Carlson

    (American Mathematical Society)

Abstract

In this paper we consider the existence of optimal solutions to dynamic optimization problems in which the decision variables are ordinary controls, a finite sequence of discrete controls giving rise to jump discontinuities in the state variables, and a finite sequence of decision times at which the discrete controls are implemented. The distance between two successive decision times is uniformly bounded below by a positive constant, which allow us to consider the admissible state trajectories as piecewise absolutely continuous functions. We show that for the models considered here the existence of an optimal solution can be obtained under conditions analogous to those in the work of L. Cesari and others for ordinary control problems. Examples arising in the operations research literature are presented to which the existence results apply.

Suggested Citation

  • Dean A. Carlson, 2025. "Existence of optimal controls with discrete decisions," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 351-373, June.
    • Handle: RePEc:spr:cejnor:v:33:y:2025:i:2:d:10.1007_s10100-025-00964-1
    DOI: 10.1007/s10100-025-00964-1
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    References listed on IDEAS

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    1. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.
    2. Gaimon, Cheryl, 1986. "An impulsive control approach to deriving the optimal dynamic mix of manual and automatic output," European Journal of Operational Research, Elsevier, vol. 24(3), pages 360-368, March.
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    Cited by:

    1. Gustav Feichtinger & Christophe Deissenberg & Ulrike Leopold-Wildburger, 2025. "George Leitmann’s 100th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 333-344, June.

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