Primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function

A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(root N log N log N/epsilon) for large-update methods and O(root N logN/epsilon) for small-update methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.