New predictor-corrector interior-point algorithm with AET function having inflection point

In this paper we introduce a new predictor-corrector interior-point algorithm for solving P_* (κ)-linear complementarity problems. For the determination of search directions we use the algebraically equivalent transformation (AET) technique. In this method we apply the function φ(t)=t^2-t+√t which has inflection point. It is interesting that the kernel corresponding to this AET function is neither self-regular, nor eligible. We present the complexity analysis of the proposed interior-point algorithm and we show that it's iteration bound matches the best known iteration bound for this type of PC IPAs given in the literature. It should be mentioned that usually the iteration bound is given for a fixed update and proximity parameter. In this paper we provide a set of parameters for which the PC IPA is well defined. Moreover, we also show the efficiency of the algorithm by providing numerical results.