Document Type: Research Paper

Authors

1 Department of Mathematics, School of Physical Science, Moddibo Adama University of Technology, Yola.

2 Department of Mathematics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria.

3 Department of Mathematical Sciences, Faculty of Sciences, Bayero University, Kano, Nigeria.

4 Department of Mathematics and Computer Science, Sule Lamido University, Ka n Hausa, Nigeria.

Abstract

There exist large varieties of conjugate gradient algorithms. In order to take
advantage of the attractive features of Liu and Storey (LS) and Conjugate Descent (CD) conjugate gradient methods, we suggest hy-
bridization of these methods in which the parameter
βk
is computed as a convex
combination of
β LS
k
and
β CD
k
respectively which the conjugate gradient (update) parameter was obtained from Secant
equation. The algorithm generates descent direction and when the iterates jam, the
direction satisfy sufficient descent condition. We report numerical results demon-
strating the efficiency of our method.The hybrid computational scheme outperform
or comparable with known conjugate gradient algorithms. We also show that our
method converge globally using strong Wolfe condition.

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Main Subjects