Applied Mathematical Sciences, Vol. 9, 2015, no. 140, 6969 - 6984 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.510686 Convergence Analysis of a New Conjugate Gradient Method for Unconstrained Optimization Ibrahim Abdullahi Department of Mathematical Sciences, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Johor, Malaysia Department of Mathematics, Federal University Dutse (FUD) P.M.B. 7156 Dutse, Jigawa State, Nigeria Rohanin Ahmad Department of Mathematical Sciences, Universiti Teknologi Malaysia (UTM), 81310 Johor Bahru, Johor, Malaysia Copyright c  2015 Ibrahim Abdullahi and Rohanin Ahmad. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribu- tion, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, the convergence analysis of a proposed new conjugate gradient method for unconstrained optimization problems was consid- ered. This method inherits an important property of Polak-Ribiere- Polyak (PRP). Under the exact line search condition, we established the descent condition of the method as well as the global convergence of the method. Numerical results show that our formula is effective by comparing with some existing formulas. Mathematics Subject Classification: 49M37, 13P25, 65N12, 90C52 Keywords: Unconstrained optimization, Conjugate gradient, Convergence, Descent algorithm 1 Introduction Conjugate gradient (CG) methods are characterized by strong global conver- gence properties and low memory requirement, this make them an active op-