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Zbl 1153.90019
Gowda, M.Seetharama; Sznajder, R.
Some global uniqueness and solvability results for linear complementarity problems over symmetric cones. (English)
[J] SIAM J. Optim. 18, No. 2, 461-481 (2007). ISSN 1052-6234; ISSN 1095-7189/e

Summary: This article deals with linear complementarity problems over symmetric cones. Our objective here is to characterize global uniqueness and solvability properties for linear transformations that leave the symmetric cone invariant. Specifically, we show that, for algebra automorphisms on the Lorentz space $\cal{L}^n$ and for quadratic representations on any Euclidean Jordan algebra, global uniqueness, global solvability, and the $\bbfR_0$-properties are equivalent. We also show that for Lyapunov-like transformations, the global uniqueness property is equivalent to the transformation being positive stable and positive semidefinite.

MSC 2000:: *90C33 Complementarity problems
17C55 Finite dimensional structures
15A48 Positive matrices and their generalizations
15A57 Other types of matrices

Keywords: Euclidean Jordan algebra; symmetric cone; algebra/cone automorphism; ${\bbfR}_0$-property; ${\bbfQ}$-property; $\bold{GUD}$-property

Cited in: Zbl 1258.90085

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