This paper revisits the idea of employing higher-order derivatives of interior point trajectories within an algorithmic framework. The paper carefully outlines the trajectories of relevance and introduces the importance of their expansion’s radius of convergence. This is supplemented with significant computational results, which highlight the computational potential of using higher-order algorithms for certain classes of problems. A theoretical complexity analysis also proves that a second-order trajectory-following algorithm for linear programming retains the $O(\sqrt{n}\log 1/ϵ)$ iteration dependency of current primal-dual methods.

中文翻译：

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采用中心路径类轨迹的高阶导数的内点框架：在凸二次规划中的应用

本文重新审视了在算法框架内使用内点轨迹的高阶导数的想法。论文仔细勾勒了相关性的轨迹，并介绍了它们扩展收敛半径的重要性。这辅以重要的计算结果，这些结果突出了使用高阶算法解决某些类别的问题的计算潜力。理论复杂度分析也证明了线性规划的二阶轨迹跟踪算法保留了$○(\sqrt{n}\mathrm{日志}1/\epsilon )$ 当前原始对偶方法的迭代依赖性。