Identification of the optimal active set in a noninterior continuation method for LCP

This paper concerns about the possibility of identifying the active set in a noninterior continuation method for solving the standard linear complementarity problem based on the algorithm and theory presented by Burke and Xu (J. Optim. Theory Appl. 112 ( 2002) 53). It is shown that under the assumptions of P-matrix and nondegeneracy, the algorithm requires at most O (log (beta(0) mu(0)/tau)) iterations to find the optimal active set, where beta(0) is the width of the neighborhood which depends on the initial point, mu(0) > 0 is the initial smoothing parameter, rho is a positive number which depends on the problem and the initial point, and tau is a small positive number which depends only on the problem.