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Canonical Duality Theory for Solving Non-monotone Variational Inequality Problems

  • Guoshan Liu
  • David Yang Gao
  • Shouyang Wang
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 37)

Abstract

This paper presents a canonical dual approach for solving a class of non-monotone variational inequality problems. It shows that by using the canonical dual transformation, these challenging problems can be reformulated as a canonical dual problem, which is equivalent to the primal problems in the sense that they have the same set of KKT points. Existence theorem for global optimal solutions is obtained. Based on the canonical duality theory, this dual problem can be solved via well-developed convex programming methods. Applications are illustrated with several examples.

Notes

Acknowledgements

The research of the first author (Guoshan Liu) was supported by the National Natural Science Foundation of China under its grand # 70771106 and the New Century Excellent Scholarship of Ministry of Education, China. The research of the second author (David Gao) was supported by US Air Force Office of Scientific Research under the grants FA2386-16-1-4082 and FA9550-17-1-0151.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of BusinessRenmin University of ChinaBeijingChina
  2. 2.Faculty of Science and TechnologyFederation University AustraliaBallaratAustralia
  3. 3.Laboratory of ManagementDecision and Information Systems Chinese Academy of SciencesBeijingChina

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