Some Global Uniqueness and Solvability Results for Linear Complementarity Problems Over Symmetric Cones
研究了对称锥上线性互补问题的全局唯一性和可解性，证明了在洛伦兹空间的自同构和欧几里得若尔当代数的二次表示下，全局唯一性、全局可解性与R0性质等价，并给出了李雅普诺夫型变换的等价条件。
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 $\mathcal{L}^n$ and for quadratic representations on any Euclidean Jordan algebra, global uniqueness, global solvability, and the ${\bf R}_0$-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.