SIAM Journal on Optimization, Volume 30, Issue 3, Page 2470-2500, January 2020.
In this paper, we study active set identification results for the away-step Frank--Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result. We then prove, for nonconvex objectives, a novel $O(1/\sqrt{k})$ convergence rate result and active set identification for different step sizes (under suitable assumptions on the set of stationary points). By exploiting those results, we also give explicit active set complexity bounds for both strongly convex and nonconvex objectives. While we initially consider the probability simplex as feasible set, in an appendix we show how to adapt some of our results to generic polytopes.

中文翻译：

---

主动Frank-Wolfe算法的主动集复杂度

SIAM优化杂志，第30卷，第3期，第2470-2500页，2020年1月。
在本文中，我们研究了在不同设置下步距为Frank-Wolfe算法的活动集识别结果。我们首先证明了一种局部识别属性，我们将其与收敛假设结合使用，以获得一个有效的集合识别结果。然后，对于非凸目标，我们证明了新颖的$ O（1 / \ sqrt {k}）$收敛速度结果和针对不同步长的活动集识别（在固定点集的适当假设下）。通过利用这些结果，我们还为强凸和非凸目标都给出了显式的主动集复杂度边界。虽然我们最初将概率单纯形视为可行集，但在附录中，我们展示了如何使我们的某些结果适应通用多面体。