UC Berkeley

The semidefinite linear complementarity problem (SDLCP) is a

generalization of the linear complementarity problem (LCP) in

which linear transformations replace matrices and the cone of

positive semidefinite matrices replaces the nonnegative orthant.

We study a number of linear transformation classes (some of which

are introduced for the first time) and extend several known

results in LCP theory to the SDLCPs, and in particular, results

which are related to the key properties of uniqueness, feasibility

and convexity. Finally, we introduce some new characterizations

related to the class of matrices E* and the uniqueness of

the LCPs.