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An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems

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  • Valeriya Lykina

    (Brandenburg University of Technology Cottbus-Senftenberg)

Abstract

In this paper, we deal with infinite horizon optimal control problems involving affine-linear dynamics and prove the existence of optimal solutions. The innovation of this paper lies in the special setting of the problem, precisely in the choice of weighted Sobolev and weighted Lebesgue spaces as the state and control spaces, respectively, which turns out to be meaningful for various problems. We apply the generalized Weierstraß theorem to prove the existence result. A lower semicontinuity theorem which is needed for that is shown under weakened assumptions.

Suggested Citation

  • Valeriya Lykina, 2016. "An Existence Theorem for a Class of Infinite Horizon Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 50-73, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-013-0500-8
    DOI: 10.1007/s10957-013-0500-8
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, October.
    2. Sabine Pickenhain & Valeriya Lykina, 2006. "Sufficiency Conditions for Infinite Horizon Optimal Control Problems," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 217-232, Springer.
    3. Joël Blot & Naïla Hayek, 1996. "Second-Order Necessary Conditions for the Infinite-Horizon Variational Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 979-990, November.
    4. Magill, Michael J. P., 1980. "An existence criterion for models of resource allocation over an infinite horizon," Economics Letters, Elsevier, vol. 5(3), pages 209-213.
    5. Takekuma, Shin-Ichi, 1980. "A sensitivity analysis on optimal economic growth," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 193-208, July.
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