Open AccessA decent three term conjugate gradient method with global convergence properties for large scale unconstrained optimization problems
Author(s) -
Ibtisam Masmali,
Zabidin Salleh,
Ahmad Alhawarat
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021624
Subject(s) - conjugate gradient method , term (time) , convergence (economics) , gradient descent , descent (aeronautics) , conjugate , gradient method , mathematics , nonlinear conjugate gradient method , function (biology) , scale (ratio) , mathematical optimization , representation (politics) , artificial neural network , derivation of the conjugate gradient method , computer science , algorithm , artificial intelligence , mathematical analysis , engineering , law , aerospace engineering , economic growth , biology , quantum mechanics , evolutionary biology , political science , physics , politics , economics
The conjugate gradient (CG) method is a method to solve unconstrained optimization problems. Moreover CG method can be applied in medical science, industry, neural network, and many others. In this paper a new three term CG method is proposed. The new CG formula is constructed based on DL and WYL CG formulas to be non-negative and inherits the properties of HS formula. The new modification satisfies the convergence properties and the sufficient descent property. The numerical results show that the new modification is more efficient than DL, WYL, and CG-Descent formulas. We use more than 200 functions from CUTEst library to compare the results between these methods in term of number of iterations, function evaluations, gradient evaluations, and CPU time.