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Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization

Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization

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References (36)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
DOI
10.1007/s10957-011-9960-x
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Dec 3, 2011

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