Isotonicity of the Metric Projection by Lorentz Cone and Variational Inequalities View Full Text


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Article Info

DATE

2017-02-22

AUTHORS

Dezhou Kong, Lishan Liu, Yonghong Wu

ABSTRACT

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. More... »

PAGES

117-130

References to SciGraph publications

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  • 2014-06-05. Isotone Projection Cones and Nonlinear Complementarity Problems in NONLINEAR ANALYSIS
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  • 2013-05-16. Equilibrium problems involving the Lorentz cone in JOURNAL OF GLOBAL OPTIMIZATION
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  • 2014-01-22. Best approximation and fixed-point theorems for discontinuous increasing maps in Banach lattices in FIXED POINT THEORY AND ALGORITHMS FOR SCIENCES AND ENGINEERING
  • 2015-05-01. The best approximation theorems and variational inequalities for discontinuous mappings in Banach spaces in SCIENCE CHINA MATHEMATICS
  • 2007-08. Inequalities Characterizing Coisotone Cones in Euclidean Spaces in POSITIVITY
  • 2008-04-16. Regular exceptional family of elements with respect to isotone projection cones in Hilbert spaces and complementarity problems in OPTIMIZATION LETTERS
  • 2015-07-08. Order-preservation of solution correspondence for parametric generalized variational inequalities on Banach lattices in FIXED POINT THEORY AND ALGORITHMS FOR SCIENCES AND ENGINEERING
  • 2016-10-24. Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2014-12-03. Extended Lorentz cones and mixed complementarity problems in JOURNAL OF GLOBAL OPTIMIZATION
  • 2014-09-03. A New Method for Solving Second-Order Cone Eigenvalue Complementarity Problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
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  • 1986-06. Monotonicity of metric projections onto positive cones of ordered Euclidean spaces in ARCHIV DER MATHEMATIK
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    http://scigraph.springernature.com/pub.10.1007/s10957-017-1084-5

    DOI

    http://dx.doi.org/10.1007/s10957-017-1084-5

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