Unified approach of primal-dual interior-point algorithms for a new class of AET functions

We propose new short-step interior-point algorithms (IPAs) for solving P_* (κ)-linear complementarity problems (LCPs). In order to define the search directions we use the algebraic equivalent transformation technique (AET) of the system which characterizes the central path. A novelty of the paper is that we introduce a new class of AET functions. We present the complexity analysis of the IPAs that use this general class of functions in the AET technique. Furthermore, we also deal with a special case, namely φ(t)=t^2-t+√t. This function differs from the ones used in the literature in the sense that it has inflection point. It does not belong to the class of concave functions determined by Haddou et al. Furthermore, the kernel function corresponding to this AET function is neither eligible nor self-regular kernel function. We prove that the IPAs using any member φ of this new class of AET functions have polynomial iteration complexity in the size of the problem, bit length of the integral data and in the parameter κ. Beside this, we also provide numerical results that show the efficiency of the introduced methods.