Applied Mathematics and Optimization

, Volume 43, Issue 2, pp 117–128

A Spectral Conjugate Gradient Method for Unconstrained Optimization

  • E. G. Birgin
  • J. M. Martínez

DOI: 10.1007/s00245-001-0003-0

Cite this article as:
Birgin, E. & Martínez, J. Appl Math Optim (2001) 43: 117. doi:10.1007/s00245-001-0003-0


A family of scaled conjugate gradient algorithms for large-scale unconstrained minimization is defined. The Perry, the Polak—Ribière and the Fletcher—Reeves formulae are compared using a spectral scaling derived from Raydan's spectral gradient optimization method. The best combination of formula, scaling and initial choice of step-length is compared against well known algorithms using a classical set of problems. An additional comparison involving an ill-conditioned estimation problem in Optics is presented.

Key words. Unconstrained minimization, Spectral gradient method, Conjugate gradients. AMS Classification. 49M07, 49M10, 90C06, 65K. 

Copyright information

© 2000 Springer-Verlag New York Inc.

Authors and Affiliations

  • E. G. Birgin
    • 1
  • J. M. Martínez
    • 2
  1. 1.Department of Computer Science, IME-USP, University of São Paulo, Rua do Matão, 1010 - Cidade Universitária, 05508-900 São Paulo SP, Brazil BR
  2. 2.Department of Applied Mathematics, IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil martinez@ime.unicamp.brBR

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