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Global Convergence of Conjugate Gradient Methods without Line Search

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  • Jie Sun
  • Jiapu Zhang

Abstract

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: (1) The Fletcher–Reeves method, the Hestenes–Stiefel method, and the Dai–Yuan method applied to a strongly convex LC 1 objective function; (2) The Polak–Ribière method and the Conjugate Descent method applied to a general, not necessarily convex, LC 1 objective function. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Jie Sun & Jiapu Zhang, 2001. "Global Convergence of Conjugate Gradient Methods without Line Search," Annals of Operations Research, Springer, vol. 103(1), pages 161-173, March.
    • Handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:161-173:10.1023/a:1012903105391
    DOI: 10.1023/A:1012903105391
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    Citations

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    Cited by:

    1. Shi, Zhen-Jun & Shen, Jie, 2007. "Convergence of Liu-Storey conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 182(2), pages 552-560, October.
    2. Yi-gui Ou & Guan-shu Wang, 2012. "A hybrid ODE-based method for unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 53(1), pages 249-270, September.
    3. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    4. C. Labat & J. Idier, 2008. "Convergence of Conjugate Gradient Methods with a Closed-Form Stepsize Formula," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 43-60, January.
    5. Sun, Jie & Yang, Xiaoqi & Chen, Xiongda, 2005. "Quadratic cost flow and the conjugate gradient method," European Journal of Operational Research, Elsevier, vol. 164(1), pages 104-114, July.
    6. Shao-Jian Qu & Mark Goh & Xiujie Zhang, 2011. "A new hybrid method for nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 49(3), pages 493-520, July.
    7. Rivaie, Mohd & Mamat, Mustafa & Abashar, Abdelrhaman, 2015. "A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1152-1163.

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