A Corrector-Predictor Arc-search Interior Point Algorithm for 𝑷∗(𝜿)-LCP Acting in a Wide Neighborhood of the Central Path

We propose an arc-search corrector-predictor interior point method for solving 𝑃∗(𝜅)-linear complementarity problems. The proposed algorithm searches for the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithm does not depend on the handicap 𝜅of the problem, so that it can be used for any 𝑃∗(𝜅)-linear complementarity problem. Based on the ellipse approximation of the central path and the wide neighborhood, we show that the proposed algorithm has 𝑂((1 + 𝜅)√𝑛𝐿) iteration complexity, the best-known iteration complexity obtained so far by any interior point method for solving 𝑃∗(𝜅)-linear complementarity problems. Some numerical results are presented to show the performance of the algorithm.