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Numerical Algorithms

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13.06.2019 | Original Paper

Adaptive SOR methods based on the Wolfe conditions

verfasst von: Yuto Miyatake, Tomohiro Sogabe, Shao-Liang Zhang

Erschienen in: Numerical Algorithms | Ausgabe 1/2020

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Abstract

Because the expense of estimating the optimal value of the relaxation parameter in the successive over-relaxation (SOR) method is usually prohibitive, the parameter is often adaptively controlled. In this paper, new adaptive SOR methods are presented that are applicable to a variety of symmetric positive definite linear systems and do not require additional matrix-vector products when updating the parameter. To this end, we regard the SOR method as an algorithm for minimising a certain objective function, which yields an interpretation of the relaxation parameter as the step size following a certain change of variables. This interpretation enables us to adaptively control the step size based on some line search techniques, such as the Wolfe conditions. Numerical examples demonstrate the favourable behaviour of the proposed methods.

Vorheriger Artikel Regularized dual gradient distributed method for constrained convex optimization over unbalanced directed graphs

Nächster Artikel A finite difference approximation of reduced coupled model for slightly compressible Forchheimer fractures in Karst aquifer system

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A function \(f\in \mathbb {R}^{n}\to \mathbb {R}\) is said to be strictly convex if and only if for all \(\boldsymbol {x},\boldsymbol {y}\in \mathbb {R}^{n}\) (x≠y) and λ ∈ (0, 1), it holds that f(λx + (1 − λ)y) < λf(x) + (1 − λ)f(y).

A function \(f\in \mathbb {R}^{n}\to \mathbb {R}\) is said to be coercive if and only if f(x) →∞ for ∥x∥→∞.

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Titel: Adaptive SOR methods based on the Wolfe conditions
verfasst von: Yuto Miyatake
Tomohiro Sogabe
Shao-Liang Zhang
Publikationsdatum: 13.06.2019
Verlag: Springer US
Erschienen in: Numerical Algorithms / Ausgabe 1/2020
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-019-00748-0

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