An Extension of Lemke’s Method to the Piecewise Linear Complementarity Problem

This paper gives a constructive method for finding a solution to the piecewise linear complementarily problem. The construction is essentially based on Lemke’s algorithm for solving the linear complementarily problem, and the extended algorithm does indeed generate a piecewise linear almost complementary path. A necessary and sufficient condition for the algorithm to compute a solution is a slight modification of the condition assumed by Eaves [4] for the existence of solutions to general nonlinear cases. The results presented in this paper do not depend on the particular subdivision scheme used to define the piecewise linear functions.