Identification of the Optimal Active Set in a Noninterior Continuation Method for LCP

Abstract

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\left(ρ\log {(β0μ0}/{τ})\right) iterations to find the {optimal active set}, where β0 is the width of the neighborhood which depends on the initial point, μ0> 0 is the initial smoothing parameter, ρ is a positive number which depends on the problem and the initial point, and τ is a small positive number which depends only on the problem.