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Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema

Author

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  • D. F. M. Torres

    (University of Aveiro)

  • G. Leitmann

    (University of California)

Abstract

In this note, we contrast two transformation-based methods to deduce absolute extrema and the corresponding extremizers. Unlike variation-based methods, the transformation-based methods of Carlson and Leitmann and the recent one of Silva and Torres are direct in that they permit obtaining solutions by inspection.

Suggested Citation

  • D. F. M. Torres & G. Leitmann, 2008. "Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 53-59, April.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9292-z
    DOI: 10.1007/s10957-007-9292-z
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    References listed on IDEAS

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    1. D. A. Carlson & G. Leitmann, 2005. "Coordinate Transformation Method for the Extremization of Multiple Integrals," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 523-533, December.
    2. D.A. Carlson, 2002. "An Observation on Two Methods of Obtaining Solutions to Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(2), pages 345-361, August.
    3. Dean A. Carlson & George Leitmann, 2005. "A Direct Method for Open-Loop Dynamic Games for Affine Control Systems," Springer Books, in: Alain Haurie & Georges Zaccour (ed.), Dynamic Games: Theory and Applications, chapter 0, pages 37-55, Springer.
    4. G. Leitmann, 2001. "Some Extensions to a Direct Optimization Method," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 1-6, October.
    5. Pierre Cartigny & Christophe Deissenberg, 2004. "An Extension Of Leitmann'S Direct Method To Inequality Constraints," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 15-20.
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    Citations

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    Cited by:

    1. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. A. B. Malinowska & D. F. M. Torres, 2010. "The Hahn Quantum Variational Calculus," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 419-442, December.

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