Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well.

Keywords

Stochastic vector variational inequalities, Expected residual minimization formulation, Sample average approximation

Publication Date

2016

Source Publication Title

Journal of Optimization Theory and Applications

Volume

175

Issue

2

Start Page

545

End Page

566

Publisher

Springer Verlag

Peer Reviewed

1

Copyright

The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s10957-016-0939-5

DOI

10.1007/s10957-016-0939-5

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10957-016-0939-5

ISSN (print)

00223239

ISSN (electronic)

15732878

Available for download on Saturday, December 01, 2018

Included in

Mathematics Commons

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