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A Generalized Conjugate Gradient Algorithm

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Abstract

We present modifications of the generalized conjugate gradient algorithm of Liu and Storey for unconstrained optimization problems (Ref. 1), extending its applicability to situations where the search directions are not defined. The use of new search directions is proposed and one additional condition is imposed on the inexact line search. The convergence of the resulting algorithm can be established under standard conditions for a twice continuously differentiable function with a bounded level set. Algorithms based on these modifications have been tested on a number of problems, showing considerable improvements. Comparisons with the BFGS and other quasi-Newton methods are also given.

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References

  1. Liu, Y., and Storey, C., Efficient Generalized Conjugate-Gradient Algorithms, Part 1: Theory, Journal of Optimization Theory and Applications, Vol. 69, pp. 129-137, 1991.

    Google Scholar 

  2. Fletcher, R., Practical Methods of Optimization, 2nd Edition, John Wiley, Chichester, England, 1987.

    Google Scholar 

  3. Powell, M. J. D., Nonconvex Minimization Calculations and the Conjugate Gradient Method, Numerical Analysis, Dundee, 1983; Edited by D. F. Griffiths, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, pp. 122-131, 1984.

    Google Scholar 

  4. Al-Baali, M., Descent Property and Global Convergence of the Fletcher-Reeves Method with Inexact Line Search, IMA Journal of Numerical Analysis, Vol. 5, pp. 121-124, 1985.

    Google Scholar 

  5. Goldstein, A. A., On Steepest Descent, SIAM Journal on Control, Vol. 5, pp. 147-151, 1965.

    Google Scholar 

  6. Khoda, K. M., Liu, Y., and Storey, C., Generalized Polak-Ribière Algorithm, Journal of Optimization Theory and Applications, Vol. 75, pp. 345-354, 1992.

    Google Scholar 

  7. Hu, Y. F., and Storey, C., Efficient Generalized Conjugate-Gradient Algorithms, Part 2: Implementation, Journal of Optimization Theory and Applications, Vol. 69, pp. 139-152, 1991.

    Google Scholar 

  8. Hock, W., and Schittkowski, K., Test Examples for Nonlinear Programming Codes, Springer Verlag, Berlin, Germany, 1981.

    Google Scholar 

  9. Touati-ahmed, D., and Storey, C., Efficient Hybrid Conjugate-Gradient Techniques, Journal of Optimization Theory and Applications, Vol. 64, pp. 379-397, 1990.

    Google Scholar 

  10. MorÉ, J. J., Garbow, B. S., and Hillstrom, K. E., Testing Unconstrained Optimization Software, ACM Transactions on Mathematical Software, Vol. 7, pp. 17-41, 1981.

    Google Scholar 

  11. Al-Baali, M., Variational Quasi-Newton Methods for Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 77, pp. 127-143, 1993.

    Google Scholar 

  12. Hu, Y. F., and Storey, C., Preconditioned Low-Order Newton Methods, Journal of Optimization Theory and Applications, Vol. 79, pp. 311-331, 1993.

    Google Scholar 

  13. Miele, A., and Cantrell, J. W., Study on a Memory Gradient Method for the Minimization of Functions, Journal of Optimization Theory and Applications, Vol. 3, pp. 459-470, 1969.

    Google Scholar 

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Authors and Affiliations

  1. Conselleria de Cultura, Educació i Ciència de la Generalitat Valenciana, Department of Statistics and Operations Research, University of Valencia, Valencia, Spain

    S. Sanmatías (PhD Student)

  2. Department of Statistics and Operations Research, University of Valencia, Valencia, Spain

    E. Vercher (Professor)

Authors
  1. S. Sanmatías
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  2. E. Vercher
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Sanmatías, S., Vercher, E. A Generalized Conjugate Gradient Algorithm. Journal of Optimization Theory and Applications 98, 489–502 (1998). https://doi.org/10.1023/A:1022653904717

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