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Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions. (English) Zbl 1190.90275
Summary: 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 $$O(\sqrt N \log N)\log \frac{N}{\varepsilon}$$ for large- and $$O(\sqrt N)\log \frac{N}{\varepsilon}$$ for small-update methods, respectively. Here $$N$$ denotes the number of second-order cones in the problem formulation and $$\varepsilon$$ the desired accuracy. These iteration bounds are currently the best known bounds for such methods. Numerical results show that the algorithms are efficient.

##### MSC:
 90C51 Interior-point methods 90C25 Convex programming
SeDuMi
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##### References:
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