Malaysian Journal of Mathematical Sciences, March 2016, Vol. 10(S)
Special Issue: The 10th IMT-GT International Conference on Mathematics, Statistics and its Applications 2014 (ICMSA 2014)
An Efficient Modification of Nonlinear Conjugate Gradient Method
Zabidin Salleh, Ahmad Alhawarat, Mustafa Mamat and Mohd Rivaie
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
To solve large and small scale unconstrained optimization problems, conjugate gradient method (CG) is an interesting and active method to find the optimum point for linear and nonlinear optimization functions. Wei et al. (2006) presented an efficient modification of Polak-Ribiere-Polyak (1969) formula, since it passes the global convergence properties under several lines searches with sufficient descent condition. In this paper, we depict a new positive CG method derived from above two coefficients, the new method achieves the global convergence properties with the strong Wolfe-Powel, weak Wolfe Powell, and Modified Armijo line searches. The numerical computations with the strong Wolfe-Powell line search demonstrated the efficiency of the new formula is almost superior to other modern methods.
Keywords: Inexact line search, global convergence, optimization problems, search direction
