Some Noninterior Continuation Methods for Linear Complementarity Problems

Abstract
We introduce some new path-following methods for the solution of the linear complementarity problem. We call these methods noninterior continuation methods since, in contrast to interior-point methods, not all iterates have to stay in the positive orthant. This is possible since we reformulate certain perturbed complementarity problems as a nonlinear system of equations. However, similar to interior-point methods, we also try to follow the central path. We present some conditions which guarantee the existence of this central path, prove a global convergence result for some implementable noninterior continuation methods, and report some numerical results obtained with these methods. We also prove global error bound results for the perturbed linear complernentarity problems.