Complexity of large-update interior point algorithm for [formula omitted] linear complementarity problems

Abstract

In this paper we propose a new large-update primal–dual interior point algorithm for P ∗ ( κ ) linear complementarity problems (LCPs). We extend Bai et al.’s primal–dual interior point algorithm for linear optimization (LO) problems to P ∗ ( κ ) LCPs with generalized kernel functions. New search directions and proximity functions are proposed based on a simple kernel function which is neither a logarithmic barrier nor a self-regular. We show that if a strictly feasible starting point is available, then the new large-update primal–dual interior point algorithms for solving P ∗ ( κ ) LCPs have O ( ( 1 + 2 κ ) n log n μ 0 ε ) polynomial complexity which is similar to the polynomial complexity obtained for LO and give a simple complexity analysis. This proximity function has not been used in the complexity analysis of interior point method (IPM) for P ∗ ( κ ) LCPs before.