Properties and Numerical Performance of Nonlinear Conjugate Gradient Methods Whit Modified Secant Equations and New Conjugacy Conditions

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Abdi, Javad | 2009

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 39980 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezamedin
Abstract:
Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, a new conjugacy condition proposed by Dai and Liao, considers an inexact line search scheme that reduces to the old one if the line search is exact. Based on this condition, a new conjugate gradient method was proposed that has fast convergence. Later, Yabe and Takano, based on new conjugacy condition and modified secant condition, proposed another conjugate gradient method. This method takes both the available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective function. Recently, two new conjugate gradient methods were proposed based on Dai-Liao and Yabe-Takano methods and multi-step secant condition. Here we explain these two new conjugate gradient methods, implement and run the related algorithms on MATLAB 7.4. Reported numerical results show that if the available parameters in these two methods are chosen suitably, then the methods will be much more efficient than other conjugate gradient methods.
Keywords:
Unconstrainted Optimization ; Conjuagate Gradient Method ; Line Search ; Global Convergence ; Multi-Step Secant Condition

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