Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities
© 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...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer New York LLC
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/52609 |
| _version_ | 1848758968979030016 |
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| author | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_facet | Kong, D. Liu, Lishan Wu, Yong Hong |
| author_sort | Kong, D. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | © 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. |
| first_indexed | 2025-11-14T09:52:25Z |
| format | Journal Article |
| id | curtin-20.500.11937-52609 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:52:25Z |
| publishDate | 2017 |
| publisher | Springer New York LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-526092017-09-13T15:39:23Z Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities Kong, D. Liu, Lishan Wu, Yong Hong © 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. 2017 Journal Article http://hdl.handle.net/20.500.11937/52609 10.1007/s10957-017-1084-5 Springer New York LLC restricted |
| spellingShingle | Kong, D. Liu, Lishan Wu, Yong Hong Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title | Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title_full | Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title_fullStr | Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title_full_unstemmed | Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title_short | Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities |
| title_sort | isotonicity of the metric projection by lorentz cone and variational inequalities |
| url | http://hdl.handle.net/20.500.11937/52609 |