Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities
MetadataShow full item record
© 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.
Showing items related by title, author, creator and subject.
Kong, D.; Liu, Lishan; Wu, Yong Hong (2017)© 2017 Springer Science+Business Media, LLC In this paper, as the extension of the isotonicity of the metric projection, the isotonicity characterizations with respect to two arbitrary order relations induced by cones of ...
Sun, D.; Sun, Jie (2008)We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical ...
A modified alternating direction method for convex quadratically constrained quadratic semidefinite programsSun, Jie; Zhang, S. (2010)We propose a modified alternating direction method for solving convex quadratically constrained quadratic semidefinite optimization problems. The method is a first-order method, therefore requires much less computational ...