Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization.
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| Title: | Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization. |
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| Authors: | Kobayashi, Hiroshi1 (AUTHOR), Narushima, Yasushi2 (AUTHOR) narushima@ynu.ac.jp, Yabe, Hiroshi3 (AUTHOR) |
| Source: | Optimization Methods & Software. December 2017, Vol. 32 Issue 6, p1313-1329. 17p. |
| Subjects: | Conjugate gradient methods, Secant function, Trigonometric functions, Number theory, Mathematical optimization |
| Abstract: | The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given. [ABSTRACT FROM PUBLISHER] |
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| Database: | Engineering Source |
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| Abstract: | The conjugate gradient method is an effective method for large-scale unconstrained optimization problems. Recent research has proposed conjugate gradient methods based on secant conditions to establish fast convergence of the methods. However, these methods do not always generate a descent search direction. In contrast, Y. Narushima, H. Yabe, and J.A. Ford [A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim. 21 (2011), pp. 212–230] proposed a three-term conjugate gradient method which always satisfies the sufficient descent condition. This paper makes use of both ideas to propose descent three-term conjugate gradient methods based on particular secant conditions, and then shows their global convergence properties. Finally, numerical results are given. [ABSTRACT FROM PUBLISHER] |
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| ISSN: | 10556788 |
| DOI: | 10.1080/10556788.2017.1338288 |
