A DESCENT PRP CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION

It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods. Also, the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we propose a new Armijo-type line search algorit...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 9; no. 3; p. 535
Main Authors Nosratipour, H, Amini, K
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2019
Elman Hasanoglu
Subjects
Algorithms
Conjugate gradient method
Conjugates
Convergence
Convergence (Mathematics)
Descent
Mathematical research
Optimization
Optimization theory
Queuing theory
Search algorithms
Iran
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Summary:It is well known that the sufficient descent condition is very important to the global convergence of the nonlinear conjugate gradient methods. Also, the direction generated by a conjugate gradient method may not be a descent direction. In this paper, we propose a new Armijo-type line search algorithm such that the direction generated by the PRP conjugate gradient method has the sufficient descent property and ensures the global convergence of the PRP conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions. We also present some numerical results to show the efficiency of the proposed method. The results show the efficiency of the proposed method in the sense of the performance profile introduced by Dolan and More. Keywords: Unconstrained optimization, Armijo-type line search, Conjugate gradient method, sufficient descent, Global convergence. AMS Subject Classification: 90C30, 65K05
ISSN:2146-1147
2146-1147