Complexity of large-update interior point algorithm for P?(?) P ? ( ? ) linear complementarity problems
In this paper we propose a new large-update primaldual interior point algorithm for P?(?) P ? ( ? ) linear complementarity problems (LCPs). We extend Bai etal.s primaldual interior point algorithm for linear optimization (LO) problems to P?(?) P ? ( ? ) 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 primaldual interior point algorithms for solving P?(?) P ? ( ? ) LCPs have O ( ( 1 + 2 ? ) n log n ? 0 ? ) 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?(?) P ? ( ? ) LCPs before.
complexity large-update linear complementarity problem kernel function primaldual interior point method polynomial algorithm