Glasnik Matematicki, Vol. 52, No. 2 (2017), 361-375.

AN EXTENDED DAI-LIAO CONJUGATE GRADIENT METHOD WITH GLOBAL CONVERGENCE FOR NONCONVEX FUNCTIONS

Mohammad Reza Arazm, Saman Babaie-Kafaki and Reza Ghanbari

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195-363, Semnan, Iran
e-mail: mohamadreza.arazm@semnan.ac.ir

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195-363, Semnan, Iran
e-mail: sbk@semnan.ac.ir

Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box: 9177948953, Mashhad, Iran
e-mail: rghanbari@um.ac.ir


Abstract.   Using an extension of some previously proposed modified secant equations in the Dai-Liao approach, a modified nonlinear conjugate gradient method is proposed. As interesting features, the method employs the objective function values in addition to the gradient information and satisfies the sufficient descent property with proper choices for its parameter. Global convergence of the method is established without convexity assumption on the objective function. Results of numerical comparisons are reported. They demonstrate efficiency of the proposed method in the sense of the Dolan-Moré performance profile.

2010 Mathematics Subject Classification.   65K05, 90C53, 49M37.

Key words and phrases.   Unconstrained optimization, large-scale optimization, conjugate gradient method, sufficient descent property, nonconvexity, global convergence.


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DOI: 10.3336/gm.52.2.12


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