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Trigonometric Convex Underestimator for the Base Functions in Fourier Space

Author

Listed:
  • S. Caratzoulas

    (University of Delaware)

  • C. A. Floudas

    (Princeton University)

Abstract

A three-parameter (a, b, xs) convex underestimator of the functional form φ(x) = -a sin[k(x-xs)] + b for the function f(x) = α sin(x+s), x ∈ [xL, xU], is presented. The proposed method is deterministic and guarantees the existence of at least one convex underestimator of this functional form. We show that, at small k, the method approaches an asymptotic solution. We show that the maximum separation distance of the underestimator from the minimum of the function grows linearly with the domain size. The method can be applied to trigonometric polynomial functions of arbitrary dimensionality and arbitrary degree. We illustrate the features of the new trigonometric underestimator with numerical examples.

Suggested Citation

  • S. Caratzoulas & C. A. Floudas, 2005. "Trigonometric Convex Underestimator for the Base Functions in Fourier Space," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 339-362, February.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:2:d:10.1007_s10957-004-0940-2
    DOI: 10.1007/s10957-004-0940-2
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    Cited by:

    1. Jung-Fa Tsai & Ming-Hua Lin, 2011. "An Efficient Global Approach for Posynomial Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 23(3), pages 483-492, August.
    2. Hao-Chun Lu & Liming Yao, 2019. "Efficient Convexification Strategy for Generalized Geometric Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 226-234, April.
    3. Hao-Chun Lu & Han-Lin Li & Chrysanthos Gounaris & Christodoulos Floudas, 2010. "Convex relaxation for solving posynomial programs," Journal of Global Optimization, Springer, vol. 46(1), pages 147-154, January.

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