内点算法的光滑分析：终止
Smoothed Analysis of Interior-Point Algorithms: Termination
摘要：
我们进行平滑分析的终止阶段的一个通道点方法。结合Dunagan，Spielman和Teng对Renegar的邻域点算法的光滑分析，我们证明了线性规划的邻域点算法的光滑复杂性为$O (m^{3} \log (m/σ))$ .相比之下，线性规划的最坏情况复杂度的最佳已知界限是$O (m^{3} L)$，其中$L$可以与$m$一样大。我们包括一个介绍平滑分析和证明技术，已在平滑分析有用的教程。
英文摘要：
We perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar's interior-point algorithm by Dunagan, Spielman and Teng, we show that the smoothed complexity of an interior-point algorithm for linear programming is $O (m^{3} \log (m/σ))$. In contrast, the best known bound on the worst-case complexity of linear programming is $O (m^{3} L)$, where $L$ could be as large as $m$. We include an introduction to smoothed analysis and a tutorial on proof techniques that have been useful in smoothed analyses.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
