%A Menglin Cao
%A Michael C. Ferris
%T P_C matrices and the Linear Complementarity Problem
%D February 1994
%R 94-01
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X We introduce a new matrix class P_c, which consists of those
matrices M for which the solution set of the corresponding linear
complementarity problem is connected for every q in R^n. 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 the intersection of P_c and Q_0. We further investigate
the relationship of the class P_c to other known matrix classes and
show that column sufficient matrices are a subclass of P_c, as are 2x2
P_0--matrices.