Pc-matrices and the linear complementarity problem Original Research Article

We introduce a new matrix class Pc, which consists of those matrices M for which the solution set of the corresponding linear complementarity problem is connected for every q ε Rn. We consider Lemkeʹs pivotal method from the perspective of piecewise linear homotopies and normal maps and show that Lemkeʹs method processes all matrices in Pc ∩ Q0. We further investigate the relationship of the class Pc to other known matrix classes and show that column sufficient matrices are a subclass of Pc, as are 2 × 2 P0-matrices.