AI 中文总结
针对弱光滑多目标优化问题，提出无参数自适应线搜索近端梯度法，建立非凸、凸情形下的复杂度结果，非凸情形接受更宽松的 stationarity 测度，凸情形复杂度优于非凸情形。
AI 中文摘要
本文针对目标函数为弱光滑（即梯度满足Hölder连续）的多目标优化问题，提出一种带自适应线搜索的近端梯度法。该方法无需目标函数弱光滑相关参数的先验知识，具备无参数特性；其线搜索可自适应确定适配弱光滑性的合适步长。本文分析了非凸情形下的复杂度保证，与相关工作兼容，且相比现有方法，所提算法接受更宽松的 stationarity 测度；还建立了凸情形下的新复杂度结果，优于非凸情形的结果。
英文摘要
In this paper, we propose a proximal gradient method with adaptive linesearch for multiobjective optimization problems whose objective functions are weakly smooth, i.e., they have Hölder continuous gradients. The proposed method is parameter-free as we do not require prior knowledge of parameters related to the weak smoothness of the objective function; the proposed linesearch finds an appropriate step-size that adapts to the weak smoothness. The complexity guarantee analyzed in this paper for the non-convex case is compatible with related works and our algorithm accepts coercer stationarity measure compared to existing methods. We also establish a novel complexity result for the convex case which improves the one in non-convex case.
CommentsThe paper is 13 pages
