Modified LS Method for Unconstrained Optimization

Jinkui Liu, Li Zheng

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DOI: 10.4236/am.2011.26104                

Abstract

In this paper, a new conjugate gradient formula and its algorithm for solving unconstrained optimization problems are proposed. The given formula satisfies with satisfying the descent condition. Under the Grippo-Lucidi line search, the global convergence property of the given method is discussed. The numerical results show that the new method is efficient for the given test problems.

Keywords

Unconstrained Optimization, Conjugate Gradient Method, Grippo-Lucidi Line Search, Global Convergence

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Y. Liu and C. Storey, “Efficient Generalized Conjugate Gradient Algorithms. Part 1: Theory,” Journal of Optimization Theory and Applications, Vol. 69, No. 1, 1992, pp. 129-137. doi:10.1007/BF00940464
[2]	Z. F. Li, J. Chen and N. Y. Deng, “A New Conjugate Gradient Method and Its Global Convergence Properties,” Mathematical Programming, Vol. 78, 1997, pp. 375-391. doi:10.1007/BF02614362
[3]	G. H. Yu, Y. L. Zhao and Z. X. Wei, “A Descent Nonlinear Conjugate Gradient Method for Large-Scale Unconstrained Optimization,” Applied Mathematics and Com- putation, Vol. 187, No. 2, 2007, pp. 636-643. doi:10.1016/j.amc.2006.08.087
[4]	J. K. Liu, X. L. Du and K. R. Wang, “Convergence of Descent Methods with Variable Parameters,” Acta Mathematicae Applicatae Sinica, Vol. 33, No. 2, 2010, pp. 222-232.
[5]	Z. F. Li, J. Chen and N. Y. Deng, “Convergence Properties of Conjugate Gradient Methods with Goldstein Line Searches,” Journal of China Agricultural University, Vol. 1, No. 4, 1996, pp. 15-18.