Volume 54, Number 4, July-August 2020
|Page(s)||981 - 991|
|Published online||28 April 2020|
A restart scheme for the Dai–Liao conjugate gradient method by ignoring a direction of maximum magnification by the search direction matrix
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, PO Box 35195-363, Semnan, Iran
* Corresponding author: firstname.lastname@example.org
Accepted: 20 April 2019
As known, finding an effective restart procedure for the conjugate gradient methods has been considered as an open problem. Here, we aim to study the problem for the Dai–Liao conjugate gradient method. In this context, based on a singular value analysis conducted on the Dai–Liao search direction matrix, it is shown that when the gradient approximately lies in the direction of the maximum magnification by the matrix, the method may get into some computational errors as well as it may converge hardly. In such situation, ignoring the Dai–Liao search direction in the sense of performing a restart may enhance the numerical stability as well as may accelerate the convergence. Numerical results are reported; they demonstrate effectiveness of the suggested restart procedure in the sense of the Dolan–Moré performance profile.
Mathematics Subject Classification: 90C53 / 65K05 / 65F35
Key words: Nonlinear programming / unconstrained optimization / conjugate gradient method / restart strategy / maximum magnification
© EDP Sciences, ROADEF, SMAI 2020
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