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dc.contributor.authorKong, D.
dc.contributor.authorLiu, Lishan
dc.contributor.authorWu, Yong Hong
dc.identifier.citationKong, D. and Liu, L. and Wu, Y.H. 2017. Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities. Journal of Optimization Theory and Applications. 173 (1): pp. 117-130.

© 2017, Springer Science+Business Media New York.In this paper, we first discuss the geometric properties of the Lorentz cone and the extended Lorentz cone. The self-duality and orthogonality of the Lorentz cone are obtained in Hilbert spaces. These properties are fundamental for the isotonicity of the metric projection with respect to the order, induced by the Lorentz cone. According to the Lorentz cone, the quasi-sublattice and the extended Lorentz cone are defined. We also obtain the representation of the metric projection onto cones in Hilbert quasi-lattices. As an application, solutions of the classic variational inequality problem and the complementarity problem are found by the Picard iteration corresponding to the composition of the isotone metric projection onto the defining closed and convex set and the difference in the identity mapping and the defining mapping. Our results generalize and improve various recent results obtained by many others.

dc.publisherSpringer New York LLC
dc.titleIsotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities
dc.typeJournal Article
dcterms.source.titleJournal of Optimization Theory and Applications
curtin.departmentDepartment of Mathematics and Statistics
curtin.accessStatusFulltext not available

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