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Title: On Modified Conjugate Gradient Algorithms for Large-Scale Unconstrained Optimization

Abstract: The well-known class of conjugate gradient (CG) line search methods for large-scale unconstrained optimization will be analyzed and simple examples will be used to illustrate its advantages and disadvantages. Then some recent techniques will be introduced to this class to obtain certain useful properties of the modified CG methods. It will be shown, in particular, that certain techniques enforced the global convergence property to most members of the CG class of methods. Numerical results for a selection of CG algorithms and their modifications (in particular those of Fletcher-Reeves, Polak-Ribie鈥檙e and Hestenes-Stiefel methods) will be described. It will be shown that the proposed techniques improve the performance of several CG algorithms substantially.