An Improved Predictor-Corrector Interior-Point Algorithm for Linear Complementarity Problems with √𝑂(𝑛𝐿)-Iteration Complexity

Abstract

This paper proposes an improved predictor-corrector interior-point algorithm for the linear complementarity problem (LCP) based on the Mizuno-Todd-Ye algorithm. The modified corrector steps in our algorithm cannot only draw the iteration point back to a narrower neighborhood of the center path but also reduce the duality gap. It implies that the improved algorithm can converge faster than the MTY algorithm. The iteration complexity of the improved algorithm is proved to obtain √𝑂(𝑛𝐿) which is similar to the classical Mizuno-Todd-Ye algorithm. Finally, the numerical experiments show that our algorithm improved the performance of the classical MTY algorithm.