Primal–dual interior-point algorithms for second-order cone optimization based on kernel functions

We present primal–dual interior-point algorithms for second-order cone optimization based on a wide variety of kernel functions. This class of kernel functions has been investigated earlier for the case of linear optimization. In this paper we derive the iteration bounds O(NlogN)logNϵ for large- and O(N)logNε for small-update methods, respectively. Here NN denotes the number of second-order cones in the problem formulation and εε the desired accuracy. These iteration bounds are currently the best known bounds for such methods. Numerical results show that the algorithms are efficient.