New complexity analysis of a full-Newton step feasible interior-point algorithm for $$P_*(\kappa )$$P∗(κ)-LCP

In this paper, we consider a full-Newton step feasible interior-point algorithm for $$P_*(\kappa )$$P∗(κ)-linear complementarity problem. The perturbed complementarity equation $$xs=\mu e$$xs=μe is transformed by using a strictly increasing function, i.e., replacing $$xs=\mu e$$xs=μe by $$\psi (xs)=\psi (\mu e)$$ψ(xs)=ψ(μe) with $$\psi (t)=\sqrt{t}$$ψ(t)=t, and the proposed interior-point algorithm is based on that algebraic equivalent transformation. Furthermore, we establish the currently best known iteration bound for $$P_*(\kappa )$$P∗(κ)-linear complementarity problem, namely, $$O((1+4\kappa )\sqrt{n}\log \frac{n}{\varepsilon })$$O((1+4κ)nlognε), which almost coincides with the bound derived for linear optimization, except that the iteration bound in the $$P_{*}(\kappa )$$P∗(κ)-linear complementarity problem case is multiplied with the factor $$(1+4\kappa )$$(1+4κ).