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Approximation Methods in Dantzig—Wolfe Decomposition of Variational Inequalities—A Review and Extension

  • William ChungEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 513)

Abstract

In this study, we review some approximation methods being used in Dantzig-Wolfe (DW) decomposition method for variational inequalities (VI). After applying DW decomposition method, the decomposed VI consists of one VI subproblem (sub-VI) and one VI master problem (master-VI). In each decomposition computational loop, we need to use an iterative method to solve both sub-VI and master-VI individually. To improve the computational efficiency, approximation methods in solving sub-VI or master-VI (not both) are used from the literature. Under the approximation methods, the approximate sub-VI is a LP or NLP. On the other hand, master-VI is approximately solved until a condition being met. Since both approximation methods for sub-VI and master-VI were developed separately, there is a knowledge gap that if both approximation methods can be applied at the same time in solving VI with DW decomposition method. The current study is to fill this gap. That is, we propose to apply both approximation methods of sub-VI and master-VI in one DW decomposition loop. An illustrative application is provided.

Keywords

Approximation Dantzig-Wolfe decomposition Variational inequalities 

Notes

Acknowledgements

Financial support for Chung’s work came from the Research Grants Council of Hong Kong S.A.R., China (CityU 11505016).

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Management SciencesCity University of Hong KongHong KongChina

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