An infeasible full-NT step IPM for horizontal linear complementarity problem over Cartesian product of symmetric cones

Abstract

In this paper, we generalize Darvay’s technique for linear programming to horizontal linear complementarity problem over the Cartesian product of symmetric cones, or briefly Cartesian -SCHLCP, using Euclidean Jordan algebras. This problem is a comprehensive optimization problem over symmetric cones, so that handling this problem removes the necessity of dealing with many other ones. This paper is among the first ones which study interior point methods (IPMs) for the generic Cartesian -SCHLCP problems. The symmetrization of the search directions used in this paper is based on the Nesterov–Todd (NT) scaling scheme, and only full-NT steps are used at each iteration. So, line searches are not longer needed. The derived complexity bound matches the best obtained one for infeasible IPMs with small updates.