A nonmonotone scaled conjugate gradient algorithm for large-scale unconstrained optimization

This paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden-Fletcher-Goldfarb-Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive prop...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 95; no. 11; pp. 2212 - 2228
Main Authors: Ou, Yigui, Zhou, Xin
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2018
Taylor & Francis Ltd
Subjects:
Algorithms
Conjugate gradient method
Conjugates
Convergence
convergence analysis
Iterative methods
nonmonotone line search
numerical comparisons
Optimization
Queuing theory
scaled conjugate gradient algorithm
Unconstrained optimization
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:This paper proposes a nonmonotone scaled conjugate gradient algorithm for solving large-scale unconstrained optimization problems, which combines the idea of scaled memoryless Broyden-Fletcher-Goldfarb-Shanno preconditioned conjugate gradient method with the nonmonotone technique. An attractive property of the proposed method is that the search direction always provides sufficient descent step at each iteration. This property is independent of the line search used. Under appropriate assumptions, the method is proven to possess global convergence for nonconvex smooth functions, and R-linear convergence for strongly convex functions. Preliminary numerical results and related comparisons show the efficiency of the proposed method in practical computation.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2017.1368498