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A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control

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  • Naïla Hayek

    (Université Paris 2 Panthéon-Assas)

Abstract

This paper generalizes to multiobjective optimization the notion of mixed problems as Philippe Michel calls it for single-objective optimization. This notion is then applied to a multiobjective control problem under constraints in the discrete time framework to obtain strong Pontryagin maximum principles in the finite-horizon case. The infinite-horizon case is also treated with conditions ensuring that the multipliers associated to the objective functions are not all zero.

Suggested Citation

  • Naïla Hayek, 2011. "A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 498-515, September.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:3:d:10.1007_s10957-011-9850-2
    DOI: 10.1007/s10957-011-9850-2
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    References listed on IDEAS

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    1. Blot, J. & Chebbi, H., 2000. "Discrete time Pontryagin Principles with Infinite Horizon," Papiers d'Economie Mathématique et Applications 2000.20, Université Panthéon-Sorbonne (Paris 1).
    2. HALKIN, Hubert, 1974. "Necessary conditions for optimal control problems with infinite horizons," LIDAM Reprints CORE 193, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-272, March.
    4. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    5. Gerhard Sorger, 2005. "A dynamic common property resource problem with amenity value and extraction costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 3-19, March.
    6. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
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    Cited by:

    1. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.
    2. Nguyen Thi Toan & Le Quang Thuy & Nguyen Tuyen & Yi-Bin Xiao, 2021. "Second-order KKT optimality conditions for multiobjective discrete optimal control problems," Journal of Global Optimization, Springer, vol. 79(1), pages 203-231, January.

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