Canonical Duality Theory for Solving Non-monotone Variational Inequality Problems
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.
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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