A new class of nonlinear conjugate gradient coefficients with exact and inexact line searches

Published on Oct 1, 2015in Applied Mathematics and Computation4.091
· DOI :10.1016/J.AMC.2015.07.019
Mohd Rivaie8
Estimated H-index: 8
(UiTM: Universiti Teknologi MARA),
Mustafa Mamat16
Estimated H-index: 16
(UniSZA: Universiti Sultan Zainal Abidin),
Abdelrhaman Abashar4
Estimated H-index: 4
(Red Sea University)
Conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. In this paper, we propose a new family of CG coefficients (βk) that possess sufficient descent conditions and global convergence properties. This new βk is an extension of the already proven β k RMIL from Rivaie et al. 19 (A new class of nonlinear conjugate gradient coefficient with global convergence properties, Appl. Math. Comp. 218(2012) 11323-11332). Global convergence result is established using both exact and inexact line searches. Numerical results show that the performance of the new proposed formula is quite similar to β k RMIL and suited to both line searches. Importantly, the performance of this βk is more efficient and superior than the other well-known βk.
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