Complexity analysis of a predictor-corrector interior-point algorithm for P*(κ)-weighted linear complementarity problems

This paper aims at a predictor-corrector interior-point algorithm for solving weighted linear complementarity problem with P*(κ)-matrices, which is a variant of weighted complementarity problem and has wide applications in science, engineering, and economics. We first apply the algebraic equivalent transformation technique, and then use the identity function to determine the new search directions. Under suitable conditions, the feasibility and convergence of the algorithm are established. Moreover, we show that the proposed algorithm has polynomial-time complexity. As far as we know, this is the first predictor-corrector interior-point algorithm for P*(κ)-weighted linear complementarity problem based on the above-mentioned search directions. Preliminary numerical results demonstrate that our algorithm performs well and efficiently on the test problems.