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Zbl 1218.90196
Jeyaraman, I.; Vetrivel, V.
On the Lipschitzian property in linear complementarity problems over symmetric cones. (English)
[J] Linear Algebra Appl. 435, No. 4, 842-851 (2011). ISSN 0024-3795

Summary: Let $V$ be a Euclidean Jordan algebra with symmetric cone $K$. We show that if a linear transformation $L$ on $V$ has the Lipschitzian property and the linear complementarity problem $LCP(L,q)$ over $K$ has a solution for every invertible $q \in V$, then $\langle L(c),c\rangle >0$ for all primitive idempotents $c$ in $V$. We show that the converse holds for Lyapunov-like transformations, Stein transformations and quadratic representations. We also show that the Lipschitzian $Q$-property of the relaxation transformation $R_{A}$ on $V$ implies that $A$ is a $P$-matrix.

MSC 2000:: *90C33 Complementarity problems
17C55 Finite dimensional structures

Keywords: Euclidean Jordan algebra; symmetric cone; complementarity problem; Lipschitzian property; relaxation transformation

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