Interior-point algorithms for symmetric cone horizontal linear complementarity problems based on a new class of algebraically equivalent transformations

Abstract

We introduce interior-point algorithms (IPAs) for solving P_* (κ)-horizontal linear complementarity problems over Cartesian product of symmetric cones. We generalize the primal-dual IPAs proposed recently by Illés et al. [21] to P_* (κ)-horizontal linear complementarity problems over Cartesian product of symmetric cones. In the algebraic equivalent transformation (AET) technique we use a modification of the class of AET functions proposed by Illés et al. [21]. In the literature, there are only few classes of functions for determination of search directions. The class of AET functions used in this paper differs from the other classes appeared in the literature. We prove that the proposed IPAs have the same complexity bound as the best known interior-point methods for solving these types of problems.