A predictor-corrector interior-point algorithm for P ∗ ( κ ) $P_{*}(\kappa )$ -horizontal linear complementarity problem

Abstract

We present a predictor-corrector path-following interior-point algorithm for P ? ( ? ) $P_*(\kappa )$ horizontal linear complementarity problem based on new search directions. In each iteration, the algorithm performs two kinds of steps: a predictor (damped Newton) step and a corrector (full Newton) step. The full Newton-step is generated from an algebraic reformulation of the centering equation, which defines the central path and seeks directions in a small neighborhood of the central path. While the damped Newton step is used to move in the direction of optimal solution and reduce the duality gap. We derive the complexity for the algorithm, which coincides with the best known iteration bound for P ? ( ? ) $P_*(\kappa )$ -horizontal linear complementarity problems.