Large-step algorithm for linear complementarity problem with new search direction

Abstract

Recently, [Darvay Zs, Takács PR: Large-step interior-point algorithm for linear optimization based on a new wide neighbourhood. Cent Eur J Oper Res. 2018;26(3):551–563] introduced a new large-step interior-point algorithm (IPA) for linear optimization (LO). The purpose of this paper is to extend this method to the class of P ∗ ( κ ) -linear complementarity problems (LCPs). First, we propose a new wide neighbourhood of the central path for LCPs, which differs from the one presented by [Ai W, Zhang S: An O ( n L ) iteration primal–dual path-following method, based on wide neighbourhoods and large updates, for monotone LCP. SIAM J Optim. 2005;16(2):400–417]. Our method uses new search directions obtained by an algebraically equivalent transformation of the system which defines the central path. We present a large-step algorithm, but we demonstrate that it has the same iteration complexity as the best short-step algorithms. Finally, we give some numerical results to prove the efficiency of the new method.