Integer Solution for Linear Complementarity Problem

We consider the problem of finding an integer solution to a linear complementarity problem. We introduce the class I of matrices for which the corresponding linear complementarity problem has an integer complementary solution for every vector, q, for which it has a solution. Strong principal unimodularity forms a sufficient condition for inclusion in the class I. It is also shown to be necessary for some well-known classes of matrices, including the class of positive semidefinite matrices. This is used in deriving necessary and sufficient conditions for a convex quadratic program to have an integer optimal solution for all b and c for which it has an optimal solution. Characterizations are also derived for some other well-known classes of matrices in linear complementarity to belong to the class I. In the end, a peeling algorithm for finding integer solution for linear complementarity problems is given and related results are derived.