Descent three-term conjugate gradient methods based on secant conditions for unconstrained optimization |
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Authors: | Hiroshi Kobayashi Hiroshi Yabe |
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Affiliation: | 1. Itochu Techno-Solutions Corporation, Chiyoda-ku, Tokyo, Japan;2. Department of Applied Mathematics, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan |
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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. |
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Keywords: | unconstrained optimization three-term conjugate gradient method secant condition sufficient descent property global convergence |
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