Full Nesterov-Todd step feasible interior-point algorithm for symmetric cone horizontal linear complementarity problem based on a positive-asymptotic barrier function

We present a feasible full step interior-point algorithm to solve the horizontal linear complementarity problem defined on a Cartesian product of symmetric cones, which is not based on a usual barrier function. The full steps are scaled utilizing the Nesterov-Todd (NT) scaling point. Our approach generates the search directions leading to the full-NT steps by algebraically transforming the centring equation of the system which defines the central trajectory using the induced barrier of a so-called positive-asymptotic kernel function. We establish the global convergence as well as a local quadratic rate of convergence of our proposed method. Finally, we demonstrate that our algorithm bears a complexity bound matching the best available one for the algorithms of its kind.

Automated summary

In this study, a feasible interior-point algorithm is proposed to solve the horizontal linear complementarity problem defined on a Cartesian product of symmetric cones. The algorithm does not rely on a usual barrier function but utilizes the Nesterov-Todd scaling point to scale the full steps. The method generates search directions leading to the full-NT steps by algebraically transforming the centring equation of the system using the induced barrier of a positive-asymptotic kernel function. The global convergence and local quadratic rate of convergence of the proposed method are established.