JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GLOBAL CONVERGENCE OF AN EFFICIENT HYBRID CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GLOBAL CONVERGENCE OF AN EFFICIENT HYBRID CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION
Liu, Jinkui; Du, Xianglin;
  PDF(new window)
 Abstract
In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.
 Keywords
unconstrained optimization;conjugate gradient method;the Wolfe line search;descent property;global convergence;
 Language
English
 Cited by
 References
1.
Y. H. Dai, A nonmonotone conjugate gradient algorithm for unconstrained optimization, J. Syst. Sci. Complex. 15 (2002), no. 2, 139-145.

2.
Y. H. Dai and Y. X. Yuan, A Nonlinear conjugate gradient with a strong global convergence property, SIAM. J. Optimization 10 (2000), 177-182.

3.
Y. H. Dai and Y. X. Yuan, Nonlinear Conjugate Gradient Method, Shanghai Scientific and Technical, Shanghai, China, 2000.

4.
Y. H. Dai and Y. X. Yuan, Convergence properties of the conjugate descent method, Adv. in Math. (China) 25 (1996), no. 6, 552-562.

5.
R. Fletcher, Practical Methods of Optimization, John Wiley & Sons, Ltd., 1987.

6.
J. C. Gilbert and J. Nocedal, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim. (1992), no. 1, 21-42.

7.
J. J. More, B. S. Garbow, and K. E. Hillstrome, Testing unconstrained optimization software, ACM Trans. Math. Software 7 (1981), no. 1, 17-41. crossref(new window)

8.
B. T. Polak, The conjugate gradient method in extreme problems, USSR Comput. Math. Math. Phys. 9 (1969), 94-112. crossref(new window)

9.
E. Polak and G. Ribiere, Note sur la convergence de methodes de directions conjuguees, Rev. Francaise Informat. Recherche Operationnelle 3 (1969) no. 16, 35-43.

10.
Z. Wei, S. Yao, and L. Liu, The convergence properties of some new conjugate gradient methods, Appl. Math. Comput. 183 (2006), no. 2, 1341-1350. crossref(new window)

11.
G. Zoutendijk, Nonlinear Programming Computational Methods, Integer and nonlinear programming, pp. 37-86. North-Holland, Amsterdam, 1970.