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Canonical Duality Theory for Solving Non-monotone Variational Inequality Problems

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Canonical Duality Theory

Part of the book series: Advances in Mechanics and Mathematics ((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.

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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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Authors and Affiliations

  1. School of Business, Renmin University of China, Beijing, 100872, China

    Guoshan Liu

  2. Faculty of Science and Technology, Federation University Australia, Ballarat, VIC, 3353, Australia

    David Yang Gao

  3. Laboratory of Management, Decision and Information Systems Chinese Academy of Sciences, Beijing, 100084, China

    Shouyang Wang

Authors
  1. Guoshan Liu
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  2. David Yang Gao
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  3. Shouyang Wang
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Corresponding author

Correspondence to Guoshan Liu .

Editor information

Editors and Affiliations

  1. Faculty of Science and Technology, Federation University Australia, Mt. Helen, Victoria, Australia

    David Yang Gao

  2. Department of Computer, Control, and Managment Engineering, Sapienza University of Rome, Rome, Roma, Italy

    Vittorio Latorre

  3. Faculty of Science and Technology, Federation University Australia, Mt. Helen, Victoria, Australia

    Ning Ruan

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Liu, G., Gao, D.Y., Wang, S. (2017). Canonical Duality Theory for Solving Non-monotone Variational Inequality Problems. In: Gao, D., Latorre, V., Ruan, N. (eds) Canonical Duality Theory. Advances in Mechanics and Mathematics, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-319-58017-3_7

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