Accelerated Hybrid Conjugate Gradient Algorithm with Modified Secant Condition

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Soleimani Kourandeh, Aria | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41855 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezamoddin
Abstract:
Conjugate gradient methods are useful for large scale nonlinear optimization problem, because they avoid the storage of any matrices. In this thesis, we have investigated an accelerated hybrid conjugate gradient algorithm, recently proposed in the literature. The combining parameter is calculated so that the corresponding direction to the conjugate gradient algorithm, while satisfies the modified secant condition, is a Newton direction. It is shown that for uniformly convex functions and for general nonlinear functions the algorithm with strong Wolfe line search is globally convergent. The algorithm uses an accelerated approach for the reduction of the objective function values by modifying the steplengths along the iterations. The algorithm was implemented in MATLAB, tested on several problems, and compared with the performance of other common algorithms
Keywords:
Unconstrainted Optimization ; Modified Secant Condition ; Hybrid Conjugate Gradient Method ; Newton Direction

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