A New Descent Nonlinear Conjugate Gradient Method for Unconstrained Optimization
Hao Fan, Zhibin Zhu, Anwa Zhou
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DOI: 10.4236/am.2011.29154   PDF    HTML     5,344 Downloads   10,757 Views   Citations

Abstract

In this paper, a new nonlinear conjugate gradient method is proposed for large-scale unconstrained optimization. The sufficient descent property holds without any line searches. We use some steplength technique which ensures the Zoutendijk condition to be held, this method is proved to be globally convergent. Finally, we improve it, and do further analysis.

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H. Fan, Z. Zhu and A. Zhou, "A New Descent Nonlinear Conjugate Gradient Method for Unconstrained Optimization," Applied Mathematics, Vol. 2 No. 9, 2011, pp. 1119-1123. doi: 10.4236/am.2011.29154.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] M. Al-Baali, “Descent Property and Global Convergence of the Fletcher-Reeves Method with Inexact Line Search,” IMA Journal of Numerical Analysis, Vol. 5, No. 1, 1985, pp. 121-124. doi:10.1093/imanum/5.1.121
[2] Y. F. Hu and C. Storey, “Global Convergence Result for Conjugate Gradient Method,” Journal of Optimization Theory and Applications, Vol. 71, No. 2, 1991, pp. 399-405. doi:10.1007/BF00939927
[3] G. Yu, Y. Zhao and Z. Wei, “A Descent Nonlinear Conjugate Gradient Method for Large-Scale Unconstrained Optimization,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 636-643. doi:10.1016/j.amc.2006.08.087
[4] Z. Wei, S. Yao and L. Liu, “The Convergence Properties of Some New Conjugate Gradient Methods,” Applied Mathematics and Computation, Vol. 183, No. 2, 2006, pp. 1341-1350. doi:10.1016/j.amc.2006.05.150
[5] G. Zoutendijk, “Nonlinear Programming, Computational Me-thods,” In: J. Abadie, Ed., Integer and Nonlinear Programming, Amsterdam, 1970, pp. 37-86.
[6] J. C. Gilbert and J. Nocedal, “Global Convergence Properties of Conjugate Gradient Methods for Optimization,” SIAM Journal Optimization, Vol. 2, No. 1, 1992, pp. 21-42. doi:10.1137/0802003
[7] Y. H. Dai and Y. Yuan, “Nonlinear Conjugate Gradient Me-thods,” Shanghai Scientific and Technical Publishers, Shanghai, 1998, pp. 37-48.
[8] W. Hock and K. Schittkowski, “Test Examples for Nonlinear Programming Codes,” Journal of Optimization Theory and Applications, Vol. 30, No. 1, 1981, pp. 127-129. doi:10.1007/BF00934594

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