Pc-matrices and the linear complementarity problem

AbstractWe 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 Lemke's pivotal method from the perspective of piecewise linear homotopies and normal maps and show that Lemke's 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