Interior-point method for second-order cone programming based on a simple kernel function

Interior-point methods not only are the most effective methods in practice but also have polynomial-time complexity. In this paper we present a primal-dual interior-point algorithm for second-order cone programming problems based on a simple kernel function. We derive the iteration bounds O(nlogε/n) and O(√nlogε/n) for large- and small-update methods, respectively, which are as good as those in the linear programming.