On the Modifications of a Broyden's Single Parameter Rank-Two Quasi-Newton Method for Unconstrained Minimization
The thesis concerns mainly in finding the numerical solution of non-linear unconstrained problems. We consider a well-known class of optimization methods called the quasi-Newton methods, or variable metric methods. In particular, a class of quasi-Newton method named Broyden's single parameter r...
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| Formaat: | Thesis |
| Taal: | English |
| Gepubliceerd in: |
1999
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| Online toegang: | http://ethesis.upm.edu.my/id/eprint/4158/1/FSAS_1999_7_F.pdf |
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| Samenvatting: | The thesis concerns mainly in finding the numerical solution of non-linear unconstrained problems. We consider a well-known class of optimization methods called the quasi-Newton methods, or variable metric methods. In particular, a class of quasi-Newton method named Broyden's single parameter rank two method is focussed. We also investigate the global convergence properties for some step-length procedures. Immediately from the investigations, a global convergence proof of the Armijo quasi-Newton method is given. Some preliminary modifications and numerical experiments are carried out to gain useful numerical experiences for the improvements of the quasi-Ne"-'ton updates.We then derived two improvement techniques: the first we employ a switching criteria between quasi-Newton Broyden-Fletcher-Goldfrab-Shanno or BFGS and steepest descent direction and in the second we introduce a reduced trace-norm condition BFGS update. The thesis includes results illustrating the numerical performance of the modified methods on a chosen set of test problems. Limitations and some possible extensions are also given to conclude this thesis. |
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