A constructive characterization ofQo-matrices with nonnegative principal minors

In [2] we characterized the class of matrices with nonnegative principla minors for which the linear-complementarity problem always has a solution. That class is contained in the one we study here. Our main result gives a finitely testable set of necessary and sufficient conditions under which a matrix with nonnegative principal minors has the property that if a corresponding linear complementarity problem is feasible then it is solvable. In short, we constructively characterize the matrix class known asQo∩Po.