An n-th section line search in conjugate gradient method for small-scale unconstrained optimization

Muhammad Imza Fakhri, Mohd Rivaie Mohd Ali, Ibrahim Jusoh


Conjugate Gradient (CG) methods are well-known method for solving unconstrained optimization problem and popular for its low memory requirement. A lot of researches and efforts have been done in order to improve the efficiency of this CG method. In this paper, a new inexact line search is proposed based on Bisection line search. Initially, Bisection method is the easiest method to solve root of a function. Thus, it is an ideal method to employ in CG method. This new modification is named n-th section. In a nutshell, this proposed method is promising and more efficient compared to the original Bisection line search. 


Unconstrained Optimization; Conjugate Gradient; Bisection; Line Search

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