A Truncated Descent HS Conjugate Gradient Method and Its Global Convergence | Zendy

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A Truncated Descent HS Conjugate Gradient Method and Its Global Convergence

Author(s) -

Wanyou Cheng,

Zongguo Zhang

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/875097

Subject(s) - line search , convergence (economics) , conjugate gradient method , mathematics , descent (aeronautics) , gradient descent , mathematical optimization , gradient method , property (philosophy) , nonlinear conjugate gradient method , computer science , artificial neural network , philosophy , computer security , epistemology , aerospace engineering , machine learning , economics , engineering , radius , economic growth

Recently, Zhang (2006) proposed a three-term modified HS (TTHS) method for unconstrained optimization problems. An attractive property of the TTHS method is that thedirection generated by the method is always descent. This property is independent of theline search used. In order to obtain the global convergence of the TTHS method, Zhangproposed a truncated TTHS method. A drawback is that the numerical performance of thetruncated TTHS method is not ideal. In this paper, we prove that the TTHS method withstandard Armijo line search is globally convergent for uniformly convex problems. Moreover,we propose a new truncated TTHS method. Under suitable conditions, global convergence isobtained for the proposed method. Extensive numerical experiment show that the proposedmethod is very efficient for the test problems from the CUTE Library

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