Abstract
Unconstrained optimization problems can be solved by using few popular methods such as Conjugate Gradient (CG) method, Steepest Descent (SD) Method and Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. The simplest solving method is by using SD method but nowadays CG method is used worldwide due to its convergence analysis. A few of unconstrained optimization problems with several different variables are used to prove the global convergence result of new spectral conjugate gradient to be compared with five most common k proposed by the early researches by using inexact line search.
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