Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras

J. Tao ()
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J. Tao: Loyola University Maryland

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 3, No 9, 575-596

Abstract: Abstract Motivated by the equivalence of the strict semimonotonicity property of the matrix A and the uniqueness of the solution to the linear complementarity problem LCP(A,q) for q∈R + n , we study the strict semimonotonicity (SSM) property of linear transformations on Euclidean Jordan algebras. Specifically, we show that, under the copositive condition, the SSM property is equivalent to the uniqueness of the solution to LCP(L,q) for all q in the symmetric cone K. We give a characterization of the uniqueness of the solution to LCP(L,q) for a Z transformation on the Lorentz cone ℒ + n . We study also a matrix-induced transformation on the Lorentz space ℒ n .

Keywords: Euclidean Jordan algebra; P property; SSM property; Copositiveness; Complementarity problem; R0 property; Q property; Z property; GUS property (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-009-9611-7

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