# American Institute of Mathematical Sciences

April  2017, 13(2): 649-658. doi: 10.3934/jimo.2016038

## A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update

 1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195–363, Semnan, Iran 2 Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran

* Corresponding author: Saman Babaie–Kafaki

Received  November 2014 Revised  December 2015 Published  May 2016

Hybridizing the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Dai and Liao based on the scaled memoryless BFGS update, a one–parameter class of four–term conjugate gradient methods is proposed. It is shown that the suggested class of conjugate gradient methods possesses the sufficient descent property, without convexity assumption on the objective function. A brief global convergence analysis is made for uniformly convex objective functions. Results of numerical comparisons are reported. They demonstrate efficiency of a method of the proposed class in the sense of the Dolan–Moré performance profile.

Citation: Saman Babaie–Kafaki, Reza Ghanbari. A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update. Journal of Industrial & Management Optimization, 2017, 13 (2) : 649-658. doi: 10.3934/jimo.2016038
##### References:

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##### References:
Total number of function and gradient evaluations performance profiles for NMDL1, NMDL2, NMDL3 and MDL
CPU time performance profiles for NMDL1, NMDL2, NMDL3 and MDL
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