Isotonicity of the Metric Projection and Complementarity Problems in Hilbert Spaces

Dezhou Kong (), Lishan Liu () and Yonghong Wu ()
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Dezhou Kong: Shandong Agricultural University
Lishan Liu: Qufu Normal University
Yonghong Wu: Curtin University

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 3, 355 pages

Abstract: Abstract 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 the metric projection operator are studied in Hilbert spaces, when one cone is a subdual cone and some relations between the two orders hold. Moreover, if the metric projection is not isotone in the whole space, we prove that the metric projection is isotone in some domains in both Hilbert lattices and Hilbert quasi-lattices. By using the isotonicity characterizations with respect to two arbitrary order relations of the metric projection, some solvability and approximation theorems for the complementarity problems are obtained. Our results generalize and improve various recent results in the field of study.

Keywords: Cone; Isotonicity; Metric projection; Complementarity problem; Quasi-lattice; 47H07; 39B62; 47J20; 47H10; 49J40 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-017-1162-8

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