A Mizuno–Todd–Ye type predictor–corrector algorithm for sufficient linear complementarity problems

We analyze a version of the Mizuno–Todd–Ye predictor–corrector interior point algorithm for the P∗(κ)P∗(κ)-matrix linear complementarity problem (LCP). We assume the existence of a strictly positive feasible solution. Our version of the Mizuno–Todd–Ye predictor–corrector algorithm is a generalization of Potra’s [F.A. Potra, The Mizuno–Todd–Ye algorithm in a larger neighborhood of the central path, European Journal of Operational Research 143 (2002) 257–267] results on the LCP with P∗(κ)P∗(κ)-matrices. We are using a ∥v−1 − v∥ proximity measure like Potra to derive iteration complexity result for this algorithm . Our algorithm is different from Miao’s method [J. Miao, A quadratically convergent O((κ+1)nL)-iteration algorithm for the P∗(κ  )-matrix linear complementarity problem, Mathematical Programming 69 (1995) 355–368] in both the proximity measure used and the way of updating the centrality parameter. Our analysis is easier than the previously stated results. We also show that the iteration complexity of our algorithm is O((1+κ)32nL).