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A Spectral Conjugate Gradient Method for Unconstrained Optimization

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Abstract.

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.

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Authors and Affiliations

  1. Department of Computer Science,IME-USP, University of São Paulo, Rua do Matão, 1010 - Cidade Universitária,05508-900 São Paulo SP, Brazil egbirgin@ime.usp.br , Brazil

    E. G. Birgin

  2. Department of Applied Mathematics,IMECC-UNICAMP, University of Campinas,CP 6065, 13081-970 Campinas SP, Brazil martinez@ime.unicamp.br, Brazil

    J. M. Martínez

Authors
  1. E. G. Birgin
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  2. J. M. Martínez
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Accepted 22 August 2000. Online publication 26 February 2001.

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Birgin, E., Martínez, J. A Spectral Conjugate Gradient Method for Unconstrained Optimization. Appl Math Optim 43, 117–128 (2001). https://doi.org/10.1007/s00245-001-0003-0

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  • DOI: https://doi.org/10.1007/s00245-001-0003-0

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