The algorithms of Broyden-CG for unconstrained optimization problems
The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
HIKARI Ltd.
2014
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| Subjects: | |
| Online Access: | http://eprints.unisza.edu.my/5632/1/FH02-FIK-15-02561.jpg http://eprints.unisza.edu.my/5632/ |
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| Summary: | The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi-newton method for solving optimization problem is suggested. The Broyden family formula is used as an approximation of Hessian in the hybrid method and the quasi-Newton method. Our numerical analysis provides strong evidence that our Broyden-CG method is more efficient than the ordinary Broyden method. Furthermore, we also prove that new algorithm is globally convergent and gratify the sufficient descent condition. |
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