CP-rays in simplicial cones
Murty, Katta G.; Kelly, Leroy Milton; Watson, Layne Terry
1990-03
Citation
Kelly, Leroy M.; Murty, Katta G.; Watson, Layne T.; (1990). "CP-rays in simplicial cones." Mathematical Programming 48 (1-3): 387-414. <http://hdl.handle.net/2027.42/47921>
Abstract
An interior point of a triangle is called CP-point if its orthogonal projection on the line containing each side lies in the relative interior of that side. In classical mathematics, interest in the concept of regularity of a triangle is mainly centered on the property of every interior point of the triangle being a CP-point. We generalize the concept of regularity using this property, and extend this work to simplicial cones in ℝ n , and derive necessary and sufficient conditions for this property to hold in them. These conditions highlight the geometric properties of Z-matrices. We show that these concepts have important ramifications in algorithmic studies of the linear complementarity problem. We relate our results to other well known properties of square matrices.Publisher
Springer-Verlag; The Mathematical Programming Society, Inc.
ISSN
1436-4646 0025-5610
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Article
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