TY - JOUR
T1 - Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization
AU - Sugiki, Kaori
AU - Narushima, Yasushi
AU - Yabe, Hiroshi
N1 - Funding Information:
Acknowledgements The authors would like to thank the referees for valuable comments. The second and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 21510164 of Japan Society for the Promotion of Science.
PY - 2012/6
Y1 - 2012/6
N2 - In this paper, we propose a three-term conjugate gradient method based on secant conditions for unconstrained optimization problems. Specifically, we apply the idea of Dai and Liao (in Appl. Math. Optim. 43: 87-101, 2001) to the three-term conjugate gradient method proposed by Narushima et al. (in SIAM J. Optim. 21: 212-230, 2011). Moreover, we derive a special-purpose three-term conjugate gradient method for a problem, whose objective function has a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed methods. Finally, some numerical results are given to show the performance of our methods.
AB - In this paper, we propose a three-term conjugate gradient method based on secant conditions for unconstrained optimization problems. Specifically, we apply the idea of Dai and Liao (in Appl. Math. Optim. 43: 87-101, 2001) to the three-term conjugate gradient method proposed by Narushima et al. (in SIAM J. Optim. 21: 212-230, 2011). Moreover, we derive a special-purpose three-term conjugate gradient method for a problem, whose objective function has a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed methods. Finally, some numerical results are given to show the performance of our methods.
KW - Descent search direction
KW - Global convergence
KW - Secant condition
KW - Three-term conjugate gradient method
KW - Unconstrained optimization
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U2 - 10.1007/s10957-011-9960-x
DO - 10.1007/s10957-011-9960-x
M3 - Article
AN - SCOPUS:84860638013
SN - 0022-3239
VL - 153
SP - 733
EP - 757
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -