A new class of spectral conjugate gradient methods based on a modified secant equation for unconstrained optimization

Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient...

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Vydáno v:Journal of computational and applied mathematics Ročník 239; s. 396 - 405
Hlavní autoři: Livieris, Ioannis E., Pintelas, Panagiotis
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.02.2013
Témata:
Computation
Conjugate gradient method
Convergence
Curvature
Global convergence
Line search
Mathematical analysis
Mathematical models
Modified secant equation
Optimization
Searching
Spectral conjugate gradient methods
Sufficient descent property
Line search
Modified secant equation
Global convergence
Spectral conjugate gradient methods
Sufficient descent property
ISSN:0377-0427, 1879-1778
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Shrnutí:Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of spectral conjugate gradient methods which ensures sufficient descent independent of the accuracy of the line search. Moreover, an attractive property of our proposed methods is that they achieve a high-order accuracy in approximating the second order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. [S. Babaie-Kafaki, R. Ghanbari, N. Mahdavi-Amiri, Two new conjugate gradient methods based on modified secant equations, Journal of Computational and Applied Mathematics 234 (2010) 1374–1386]. Further, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness.
Bibliografie:ObjectType-Article-2
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.09.007