A modified spectral conjugate gradient method for solving unconstrained minimization problems
The development a modified spectral conjugate gradient method for solving unconstrained minimization problem is considered in this paper. A new Conjugate (update) parameter is obtained by the idea of Dai-Kou's technique for generating conjugate parameters. A new spectral parameter is also presented based on quasi-Newton direction and quasi-Newton condition. Under the strong Wolfe line search, the proposed method is proved to be globally convergent. Numerical results showed that the algorithm takes lesser number of iteration to obtain the minimum of a given function compared to the method Loannis and Panagiotis’s spectral CGM  (LP for short), Birgin and Martinez’s spectral CGM  (BM for short), and Jinbao, Qian, Xianzhen, Youfang and Jianghua’s spectral CGM  ( JQXYJ for short). We hereby recommend this method for the solution of both linear and Non-linear Unconstrained optimization problem.
Keywords: Unconstrained minimization problem, Spectral conjugate gradient method, Global convergence, numerical results.
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