On the convergence of the iteration sequence of infeasible path following algorithms for linear complementarity problems

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problems is analyzed and sufficient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The computational complexity of the latter method is discussed in detail and its local convergent rate is analyzed. The primal–dual gap of the iterates produced by this method is superlinearly convergent to zero. A variant of the method has quadratic convergence.