Properties of Classes of Linear Transformations in the Semidefinite Linear Complementarity Problem

The semidefinite linear complementarity problem (SDLCP) is ageneralization of the linear complementarity problem (LCP) inwhich linear transformations replace matrices and the cone ofpositive semidefinite matrices replaces the nonnegative orthant.We study a number of linear transformation classes (some of whichare introduced for the first time) and extend several knownresults in LCP theory to the SDLCPs, and in particular, resultswhich are related to the key properties of uniqueness, feasibilityand convexity. Finally, we introduce some new characterizationsrelated to the class of matrices E* and the uniqueness ofthe LCPs