Open AccessSome generalized three-term conjugate gradient methods based on CD approach for unconstrained optimization problems
Author(s) -
Ladan Arman,
Yuanming Xu,
Liping Liu
Publication year - 2021
Publication title -
technium
Language(s) - English
Resource type - Journals
ISSN - 2668-778X
DOI - 10.47577/technium.v3i2.1983
Subject(s) - conjugate gradient method , nonlinear conjugate gradient method , gradient descent , line search , term (time) , conjugate , derivation of the conjugate gradient method , convergence (economics) , conjugate residual method , gradient method , descent (aeronautics) , mathematical optimization , mathematics , line (geometry) , computer science , algorithm , artificial intelligence , artificial neural network , mathematical analysis , geometry , physics , computer security , quantum mechanics , meteorology , economics , radius , economic growth
In this paper, based on the efficient Conjugate Descent (CD) method, two generalized CD algorithms are proposed to solve the unconstrained optimization problems. These methods are three-term conjugate gradient methods which the generated directions by using the conjugate gradient parameters and independent of the line search satisfy in the sufficient descent condition. Furthermore, under the strong Wolfe line search, the global convergence of the proposed methods are proved. Also, the preliminary numerical results on the CUTEst collection are presented to show effectiveness of our methods.