A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization
The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method h...
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| Format: | Thesis |
| Language: | English English |
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2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/7547/ http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf |
| _version_ | 1848840625192960000 |
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| author | Chen, Chuei Yee |
| author_facet | Chen, Chuei Yee |
| author_sort | Chen, Chuei Yee |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method has been widely used in large scale unconstrained optimization due to its effectiveness. However, a major drawback of the L-BFGS method is that it can be very slow on certain type of problems. Scaling and preconditioning have been used to boost the performance of the L-BFGS method.
In this study, a class of diagonally preconditioned L-BFGS method will be proposed. Contrary to the standard L-BFGS method where its initial inverse Hessian approximation is the identity matrix, a class of diagonal preconditioners has been derived based upon the weak-quasi-Newton relation with an additional parameter. Choosing different parameters leads the research to some well-known diagonal updating formulae which enable the R-linear convergent for the L-BFGS method. Numerical experiments were performed on a set of large scale unconstrained minimization problem to examine the impact of each choice of parameter. The computational results suggest that the proposed diagonally preconditioned L-BFGS methods outperform the standard L-BFGS method without any preconditioning. Finally, we discuss on the impact of the diagonal preconditioners on the L-BFGS method as compared to the standard L-BFGS method in terms of the number of iterations, the number of function/gradient evaluations and the CPU time in second. |
| first_indexed | 2025-11-15T07:30:19Z |
| format | Thesis |
| id | upm-7547 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T07:30:19Z |
| publishDate | 2009 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-75472013-05-27T07:35:31Z http://psasir.upm.edu.my/id/eprint/7547/ A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization Chen, Chuei Yee The focus of this thesis is to diagonally precondition on the limited memory quasi-Newton method for large scale unconstrained optimization problem. Particularly, the centre of discussion is on diagonally preconditioned limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method. L-BFGS method has been widely used in large scale unconstrained optimization due to its effectiveness. However, a major drawback of the L-BFGS method is that it can be very slow on certain type of problems. Scaling and preconditioning have been used to boost the performance of the L-BFGS method. In this study, a class of diagonally preconditioned L-BFGS method will be proposed. Contrary to the standard L-BFGS method where its initial inverse Hessian approximation is the identity matrix, a class of diagonal preconditioners has been derived based upon the weak-quasi-Newton relation with an additional parameter. Choosing different parameters leads the research to some well-known diagonal updating formulae which enable the R-linear convergent for the L-BFGS method. Numerical experiments were performed on a set of large scale unconstrained minimization problem to examine the impact of each choice of parameter. The computational results suggest that the proposed diagonally preconditioned L-BFGS methods outperform the standard L-BFGS method without any preconditioning. Finally, we discuss on the impact of the diagonal preconditioners on the L-BFGS method as compared to the standard L-BFGS method in terms of the number of iterations, the number of function/gradient evaluations and the CPU time in second. 2009 Thesis NonPeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf Chen, Chuei Yee (2009) A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization. Masters thesis, Universiti Putra Malaysia. Mathematical optimization - Case studies English |
| spellingShingle | Mathematical optimization - Case studies Chen, Chuei Yee A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title | A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title_full | A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title_fullStr | A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title_full_unstemmed | A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title_short | A Class of Diagonally Preconditioned Limited Memory Quasi-Newton Methods for Large-Scale Unconstrained Optimization |
| title_sort | class of diagonally preconditioned limited memory quasi-newton methods for large-scale unconstrained optimization |
| topic | Mathematical optimization - Case studies |
| url | http://psasir.upm.edu.my/id/eprint/7547/ http://psasir.upm.edu.my/id/eprint/7547/1/ABS_---__FS_2009_29.pdf |