Advertisement

A Parallel, Asynchronous Method for Derivative-Free Nonlinear Programs

  • Joshua D. Griffin
  • Tamara G. Kolda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)

Abstract

Derivative-free optimization algorithms are needed to solve real-world engineering problems that have computationally expensive and noisy objective function and constraint evaluations. In particular, we are focused on problems that involve running cumbersome simulation codes with run times measured in hours. In such cases, attempts to compute derivatives can prove futile because analytical derivatives are typically unavailable and noise limits the accuracy of numerical approximations. Furthermore, the objective and constraint functions may be inherently nonsmooth, i.e., because the underlying model is nonsmooth.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Conn, A., Gould, N., Sartenaer, A., Toint, P.: Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints. SIAM J. Optimiz. 6, 674–703 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Conn, A.R., Gould, N.I.M., Toint, P.L.: A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds. SIAM J. Numer. Anal. 28, 545–572 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fukuda, K.: cdd and cddplus homepage. From McGill University, Montreal, Canada (2005), Web page: http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html
  4. 4.
    Gray, G.A., Kolda, T.G.: Algorithm 8xx: APPSPACK 4.0: Asynchronous parallel pattern search for derivative-free optimization. ACM T. Math. Software (to appear)Google Scholar
  5. 5.
    Hough, P.D., Kolda, T.G., Torczon, V.J.: Asynchronous parallel pattern search for nonlinear optimization. SIAM J. Sci. Comput. 23, 134–156 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kolda, T.G.: Revisiting asynchronous parallel pattern search for nonlinear optimization. SIAM J. Optimiz. 16, 563–586 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kolda, T.G., Lewis, R.M., Torczon, V.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kolda, T.G., Lewis, R.M., Torczon, V.: Stationarity results for generating set search for linearly constrained optimization, Tech. Rep. SAND2003-8550, Sandia National Laboratories. Albuquerque, NM and Livermore, CA (October 2003)Google Scholar
  9. 9.
    Kolda, T.G., Lewis, R.M., Torczon, V.: Convergence properties of an augmented Lagrangian direct search algorithm for optimization with a combination of general equality and linear constraints (in preparation, 2005)Google Scholar
  10. 10.
    Kolda, T.G., Torczon, V.: On the convergence of asynchronous parallel pattern search. SIAM J. Optimiz. 14, 939–964 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Lewis, R. M., Shepherd, A., Torczon, V.: Implementing generating set search methods for linearly constrained minimization, Tech. Rep. WM-CS-2005-01, Department of Computer Science, College of William & Mary, Williamsburg, Virginia (July 2005)Google Scholar
  12. 12.
    Lewis, R.M., Torczon, V.: A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds. SIAM J. Optimiz. 12, 1075–1089 (2002)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Joshua D. Griffin
    • 1
  • Tamara G. Kolda
    • 1
  1. 1.Sandia National LaboratoriesLivermoreUSA

Personalised recommendations