  Proper cones with the property that the projection onto them is isotone with
respect to the order they induce are called isotone projection cones. Isotone
projection cones and their extensions have been used to solve complementarity
problems and variational inequalities. Q-matrices are matrices with the
property that all classical linear complementarity problems defined by them are
solvable. This note will use the isotone projection cones to generate a large
class of Q-matrices. More specifically, it will be shown that the product
between a non-negative matrix with positive diagonal elements and a Stieltjes
matrix is a Q-matrix.

Optimization and Control