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The purpose of this paper is to present the capabilities of the conjugate gradient methods based on the theoretical analysis of the gradient method, the precursor of the descent methods. It indicates the geometric differences of these and the improvements made in the search for the optimal value of an objective function. Different test systems are proposed to solve, in order to obtain a solution that can determine the speed of convergence of the conjugate address proposed by Liu-Storey anddoi:10.12988/ces.2017.711189 fatcat:77klin6duzbsjlpyyp6o7gc54a