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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Vydané v:International journal of computer mathematics Ročník 95; číslo 11; s. 2212 - 2228
Hlavní autori: Ou, Yigui, Zhou, Xin
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 02.11.2018
Taylor & Francis Ltd
Predmet:
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
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Abstract 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.
AbstractList 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.
Author Ou, Yigui
Zhou, Xin
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SubjectTerms Algorithms
Conjugate gradient method
Conjugates
Convergence
convergence analysis
Iterative methods
nonmonotone line search
numerical comparisons
Optimization
Queuing theory
scaled conjugate gradient algorithm
Unconstrained optimization
Title A nonmonotone scaled conjugate gradient algorithm for large-scale unconstrained optimization
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