Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras

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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 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLoyola University MarylandBaltimoreUSA

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