Efficiency of Spectral Gradient Method in Solving Optimization Problems

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Mirzaii, Mohammad | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41917 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezamoddin
Abstract:
In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. Later, Raydan derived an interesting relationship between a gradient method and the shifted power method. This relationship allows one to establish the convergence of the Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function. With this point of view, he explained the remarkable improvement obtained by using this new choice of steplength. For some special cases, he presented some very interesting convergence rate results. Finally, he derived the preconditioned Barzilai and Borwein method. Here, we present numerical results indicating that it is an effective method, as compared to the preconditioned conjugate gradient method
Keywords:
Gradient Based Method ; Convergence Rate ; Preconditioning

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