未知分段光滑性与二次增长条件下近端束方法的全局线性收敛
Global Linear Convergence of the Proximal Bundle Method under Unknown Piecewise Smoothness and Quadratic Growth
- School of Industrial Engineering, Purdue University（普渡大学工业工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究近端束方法在保留足够多切割平面时，能利用目标函数的分段光滑结构，实现全局线性收敛，并给出理论解释。
AI中文摘要：
我们研究为什么近端束方法（PBM）在保留更多切割平面时在实践中表现更好。我们考虑具有二次增长和未知分段光滑结构的凸目标函数。我们的关键观察是，保留足够多的切割平面使PBM能够利用目标函数的分段光滑结构，并表现得如同在优化一个光滑函数。我们为PBM在保留足够多切割平面时对分段光滑目标函数的观测到的线性收敛提供了理论解释。
英文摘要：
We study why the proximal bundle method (PBM) can perform better in practice when it retains more cutting planes. We consider convex objectives with quadratic growth and an unknown piecewise-smooth structure. Our key observation is that retaining sufficiently many cutting planes allows PBM to exploit the objective's piecewise-smooth structure and behave as if it were optimizing a smooth function. We provide a theoretical explanation for the observed linear convergence of PBM on piecewise-smooth objectives when it retains sufficiently many cutting planes.
