Comparative Study of Conjugate Gradient Coefficient for Unconstrained Optimization

Conjugate gradient methods are popular in the field of unconstrained optimization. Numerous studies have been devoted recently to improve this method. In this paper three of our new propose conjugate gradient coefficient (βk) have been compared with the six most common (βk) proposed by the early researches. The first proposed method is based from the reciprocal of the summation of the eigenvalues. The second and third proposed methods are based from the modification of the original Polak-Ribiere and Hestenes-Steifel. Numerical results have shown that, our new formula for (βk) performs far better than the original formula. It is also shown to possess global convergence properties.

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