Conjugate gradient methods with sufficient descent condition for large-scale unconstrained optimization
This thesis focuses on solving conjugate gradient methods for large-scale uncon- strained optimization problems. The main objective of this study is to propose some modifications to the standard conjugate gradient methods so that its search direction satisfies the sufficient descent and the bo...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/85444/1/FS%202016%2091%20ir.pdf |
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| Summary: | This thesis focuses on solving conjugate gradient methods for large-scale uncon-
strained optimization problems. The main objective of this study is to propose
some modifications to the standard conjugate gradient methods so that its search
direction satisfies the sufficient descent and the boundedness condition. These
two conditions appear to be a natural way of guaranteeing convergence for the
conjugate gradient methods.
We also propose some techniques for improving the conjugate gradient methods.
The techniques in consideration include scaling parameters proposed by Oren
and Luenberger, preconditioner suggested by Powell and memoryless symmetric
rank one. In addition, the modified scaled conjugate gradient method is also
implemented using nonmonotone line search. The convergence results for all of
the modified conjugate gradient methods are also established.
To validate the usefulness of our proposed improvement strategies, numerical ex-
periments on a set of standard test problems were performed and presented. The
results showed that our proposed methods can be good alternatives to the conju-
gate gradient method in solving large-scale unconstrained optimization problems. |
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