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An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization

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  • Y.H. Dai

    ()

  • Y. Yuan

    ()

Abstract

Recently, we propose a nonlinear conjugate gradient method, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the weak Wolfe conditions. In this paper, we will study methods related to the new nonlinear conjugate gradient method. Specifically, if the size of the scalar β k with respect to the one in the new method belongs to some interval, then the corresponding methods are proved to be globally convergent; otherwise, we are able to construct a convex quadratic example showing that the methods need not converge. Numerical experiments are made for two combinations of the new method and the Hestenes–Stiefel conjugate gradient method. The initial results show that, one of the hybrid methods is especially efficient for the given test problems. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
  • Handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:33-47:10.1023/a:1012930416777
    DOI: 10.1023/A:1012930416777
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    Cited by:

    1. repec:spr:joptap:v:154:y:2012:i:3:d:10.1007_s10957-012-0016-7 is not listed on IDEAS
    2. Nash, John C. & Varadhan, Ravi, 2011. "Unifying Optimization Algorithms to Aid Software System Users: optimx for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i09).
    3. repec:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-016-2120-9 is not listed on IDEAS
    4. repec:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0528-4 is not listed on IDEAS
    5. repec:spr:joptap:v:159:y:2013:i:1:d:10.1007_s10957-013-0285-9 is not listed on IDEAS
    6. repec:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9505-0 is not listed on IDEAS
    7. Serge Gratton & Vincent Malmedy & Philippe Toint, 2012. "Using approximate secant equations in limited memory methods for multilevel unconstrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 967-979, April.
    8. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    9. repec:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1324-3 is not listed on IDEAS
    10. repec:eee:ecomod:v:359:y:2017:i:c:p:372-382 is not listed on IDEAS
    11. Andrei, Neculai, 2010. "Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 410-420, August.

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