Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
The column-sufficiency and row-sufficiency of the linear transformation on Hilbert spaces
Journal of Global Optimization
A Continuation Method for Nonlinear Complementarity Problems over Symmetric Cones
SIAM Journal on Optimization
Characterizations for solidness of dual cones with applications
Journal of Global Optimization
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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.