ANZIAM J. 46(E) pp.C719--C731, 2005.

Parallel Jacobi methods for derivative-free optimization on parallel or distributed processors

I. D. Coope

M. S. Macklem

(received 19 November 2004, revised 17 May 2005)

Abstract

New Jacobi-type algorithms are presented for the efficient use of parallel and distributed computing platforms in solving derivative-free optimization problems. The implementations are designed to be fault tolerant to be applicable to science and engineering problems where occasionally requests for function values may not be met and derivatives are never available. Convergence is usually achieved by introducing an elementary trust region subproblem at synchronization steps in the algorithm. This has the added advantage of handling negative curvature very conveniently.

Download to your computer

Authors

I. D. Coope
University of Canterbury, New Zealand. mailto:ian.coope@canterbury.ac.nz
M. S. Macklem
Simon Fraser University, Vancouver, Canada.

Published July 28, 2005. ISSN 1446-8735

References

  1. K. W. Brodlie. A new method for unconstrained minimization without evaluating derivatives. J. Inst. Math. Appl., 15, 385--396, 1975.
  2. I. D. Coope, C. J. Price. Frame-based methods for unconstrained optimization. Journal of Optimization Theory & Applications, 107, 261--274, 2000.
  3. I. D. Coope, C. J. Price. On the convergence of grid-based methods for unconstrained optimization. SIAM Journal on Optimization, 11, 859--869, 2001.
  4. M. S. Macklem. PhD Thesis. Simon Fraser University, forthcoming.
  5. M. J. D. Powell. An efficient method for for finding the minimum of a function of several variables without calculating derivatives. Computer Journal, 7, 155--162, 1964.
  6. A. R. Conn, N. I. M. Gould and Ph. L. Toint. Trust--Region Methods. MPS--SIAM Series on Optimization, 2000.