Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Steplengths in the extragradient type methods

Language

English

Abstract

The extragradient type methods are a class of efficient direct methods. For solving monotone variational inequalities, these methods only require function evaluation, and therefore are widely applied to black-box models. In this type of methods, the distance between the iterate and a fixed solution point decreases by iterations. Furthermore, in each iteration, the negative increment of such squared distance has a differentiable concave lower bound function without requiring any solution in its formula. In this paper, we investigate some properties for the lower bound. Our study reveals that the lower bound affords a steplength domain which guarantees the convergence of the entire algorithm. Based on these results, we present two new steplengths. One involves the projection onto the tangent cone without line search, while the other can be computed via searching the positive root of a one dimension concave lower bound function. Our preliminary numerical results confirm and illustrate the attractiveness of our contributions. © 2009 Elsevier B.V. All rights reserved.

Keywords

Black-box model, Extragradient type methods, Monotone variational inequalities, Projection

Publication Date

2010

Source Publication Title

Journal of Computational and Applied Mathematics

Volume

233

Issue

11

Start Page

2925

End Page

2939

Publisher

Elsevier

DOI

10.1016/j.cam.2009.11.037

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.cam.2009.11.037

ISSN (print)

03770427

ISSN (electronic)

18791778

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