Abstract
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 ( N log N ) log N ϵ for large- and O ( N ) log N ε for small-update methods, respectively. Here N denotes the number of second-order cones in the problem formulation and ε the desired accuracy. These iteration bounds are currently the best known bounds for such methods. Numerical results show that the algorithms are efficient.
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