Stability of the linear complementarity problem properties under interval uncertainty

Abstract: We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite number of solutions etc.) are reflected by the properties of the constraint matrix. In order that the problem has desired properties even in the uncertain environment, we have to be able to check them for all possible realizations of interval data. This leads us to the robust properties of interval matrices. In particular, we will discuss $S$-matrix, $Z$-matrix, copositivity, semimonotonicity, column sufficiency, principal nondegeneracy, $R_0$-matrix and $R$-matrix. We characterize the robust properties and also suggest efficiently recognizable subclasses.