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A New Descent Nonlinear Conjugate Gradient Method for Unconstrained Optimization
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Applied Mathematics·Volume 02 (2011)·Pages 1119–1123·Published 29 September 2011·DOI10.4236/am.2011.29154
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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.
KeywordsLarge Scale Unconstrained OptimizationConjugate Gradient MethodSufficient Descent PropertyGlobally Convergent
- 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
- 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
- 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
- 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
- G. Zoutendijk, “Nonlinear Programming, Computational Me-thods,” In: J. Abadie, Ed., Integer and Nonlinear Programming, Amsterdam, 1970, pp. 37-86.
- 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
- Y. H. Dai and Y. Yuan, “Nonlinear Conjugate Gradient Me-thods,” Shanghai Scientific and Technical Publishers, Shanghai, 1998, pp. 37-48.
- 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