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In recent times, conjugate gradient method (CG) have been broadly used to solve nonlinear unconstrained minimization problems as a result of fewer storage locations and computational expensive in dealing with large-scale problems. In this work, we present a spectral PRP CG method which derived from the CG search direction without secant condition and utilized some of the benchmark test problem functions with several variables to prove its global convergence properties and satisfies sufficient descent condition, the results are validated by exact line search techniques.

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Conjugate Gradient (CG) method have been utilised to solve nonlinear unconstrained optimization problems because of less storage locations and fewer computational cost in dealing with large-scale problems. In this paper, we present a real life application of spectral PRP Conjugate Gradient method in regression analysis, the proposed method is suitably deriving from the CG search direction without secant condition. Some benchmark functions with several variables have been use to prove the global convergence properties and satisfies sufficient descent condition. The numerical results are certifying by exact line search techniques; the method outperform the prominent least square method