Please use this identifier to cite or link to this item: http://umt-ir.umt.edu.my:8080/handle/123456789/5904
Title: An Efficient Modification Of The Hestenes-Stiefel Nonlinear Conjugate Gradient Method With Restart Property
Authors: Zabidin, Salleh
Ahmad, Alhawarat
Keywords: Conjugate Gradient Method
Wolfe-Powell Line Search
Hestenes-Stiefel Formula
Restart Condition
Performance Profile
Issue Date: 6-Apr-2016
Publisher: Journal of Inequalities and Applications
Citation: 2016;110
Abstract: The conjugate gradient (CG) method is one of the most popular methods to solve nonlinear unconstrained optimization problems. The Hestenes-Stiefel (HS) CG formula is considered one of the most efficient methods developed in this century. In addition, the HS coefficient is related to the conjugacy condition regardless of the line search method used. However, the HS parameter may not satisfy the global convergence properties of the CG method with the Wolfe-Powell line search if the descent condition is not satisfied. In this paper, we use the original HS CG formula with a mild condition to construct a CG method with restart using the negative gradient. The convergence and descent properties with the strong Wolfe-Powell (SWP) and weak Wolfe-Powell (WWP) line searches are established. Using this condition, we guarantee that the HS formula is non-negative, its value is restricted, and the number of restarts is not too high. Numerical computations with the SWP line search and some standard optimization problems demonstrate the robustness and efficiency of the new version of the CG parameter in comparison with the latest and classical CG formulas. An example is used to describe the benefit of using different initial points to obtain different solutions for multimodal optimization functions
URI: http://hdl.handle.net/123456789/5904
ISSN: 1029 242X
Appears in Collections:Journal Articles

Files in This Item:
File Description SizeFormat 
J2016-366-An efficient modification of nonlinear conjugate gradient method.pdfFulltext file1.74 MBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.