Unified Approach of Interior-Point Algorithms for P_*(\kappa )-LCPs Using a New Class of Algebraically Equivalent Transformations

Abstract

We propose new short-step interior-point algorithms (IPAs) for solving P_*(\kappa ) P ∗ ( κ ) -linear complementarity problems (LCPs). In order to define the search directions, we use the algebraic equivalent transformation (AET) technique of the system describing the central path. A novelty of the paper is that we introduce a whole, new class of AET functions for which a unified complexity analysis of the IPAs is presented. This class of functions differs from the ones used in the literature for determining search directions, like the class of concave functions determined by Haddou, Migot and Omer, self-regular functions, eligible kernel and self-concordant functions. We prove that the IPAs using any member \varphi φ of the new class of AET functions have polynomial iteration complexity in the size of the problem, in starting point’s duality gap, in the accuracy parameter and in the parameter \kappa κ .