Advertisement

Progress in Global Optimization and Shape Design

  • D. Isebe
  • B. Ivorra
  • P. Azerad
  • B. Mohammadi
  • F. Bouchette

Abstract

In this paper, we reformulate global optimization problems in terms of boundary value problems. This allows us to introduce a new class of optimization algorithms. Indeed, many optimization methods can be seen as discretizations of initial value problems for differential equations or systems of differential equations. We apply a particular algorithm included in the former class to the shape optimization of coastal structures.

Keywords

Cost Function Global Optimization Boundary Value Problem Line Search Water Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. Mohammadi and J-H. Saiac. Pratique de la simulation numérique. Dunod, 2002.Google Scholar
  2. 2.
    H. Attouch and R. Cominetti. A dynamical approach to convex minimization coupling approximation with the steepest descent method. J. Differential Equations, 128(2):519–540, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. Mohammadi and O. Pironneau. Applied Shape Optimization for Fluids. Oxford University Press, 2001.Google Scholar
  4. 4.
    A. Jameson, F. Austin, M. J. Rossi, W. Van Nostrand, and G. Knowles. Static shape control for adaptive wings. AIAA Journal, 32(9):1895–1901, 1994.CrossRefGoogle Scholar
  5. 5.
    F. Verhulst. Nonlinear differential equations and dynamical systems. Springer-Verlag., 1990.Google Scholar
  6. 6.
    D. Colton and R. Kress. Inverse acoustic and electromagnetic scattering theory. Springer-Verlag, 1992.Google Scholar
  7. 7.
    D. Isebe, P. Azerad, B. Ivorra, B. Mohammadi, and F. Bouchette. Optimal shape design of coastal structures minimizing coastal erosion. In Proceedings of workshop on inverse problems, CIRM, Marseille, 2005.Google Scholar
  8. 8.
    J. T. Kirby and R. A. Dalrymple. A parabolic equation for the combined refraction diffraction of stokes waves by mildly varying topography. J. Fluid. Mechanics., 136:443–466, 1983.CrossRefGoogle Scholar
  9. 9.
    J. T. Kirby and R. A. Dalrymple. Combined refraction/diffraction model ref/dif 1, User’s manual. Coastal and Offshore Engineering and Research, Inc., Newark, DE., January, 1985. (Revised June, 1986).Google Scholar
  10. 10.
    B. Ivorra, B. Mohammadi, D. E. Santiago, and J. G. Hertzog. Semi-deterministic and genetic algorithms for global optimization of microfluidic protein folding devices. International Journal of Numerical Method in Engineering, 66: 319–333, 2006.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • D. Isebe
    • 1
  • B. Ivorra
    • 1
  • P. Azerad
    • 1
  • B. Mohammadi
    • 1
  • F. Bouchette
    • 2
  1. 1.I3M- Universite de Montpellier IIMontpellierFrance
  2. 2.ISTEEM - Universite de Montpellier IIMontpellierFrance

Personalised recommendations