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A primal-dual interior-point algorithm for second-order cone optimization with full Nesterov-Todd step

机译:具有完整Nesterov-Todd步骤的二阶锥优化的原始对偶内点算法

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摘要

In this paper we propose a primal-dual path-following interior-point algorithm for second-order cone optimization. The algorithm is based on a new technique for finding the search directions and the strategy of the central path. At each iteration, we use only full Nesterov-Todd step. Moreover, we derive the currently best known iteration bound for the algorithm with small-update method, namely, O(root N log N/epsilon), where N denotes the number of second-order cones in the problem formulation and epsilon the desired accuracy.
机译:在本文中,我们提出了一种用于二阶锥优化的原始对偶路径跟随内点算法。该算法基于一种用于查找搜索方向和中心路径策略的新技术。在每次迭代中,我们仅使用完整的Nesterov-Todd步骤。此外,我们用小更新方法导出算法的当前最著名的迭代边界,即O(root N log N / epsilon),其中N表示问题公式中的二阶锥数,eps表示所需的精度。

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