论文标题
通过快速梯度光滑方法，用于非平滑凸优化的近端捆绑算法
Proximal bundle algorithms for nonsmooth convex optimization via fast gradient smooth methods
论文作者
论文摘要
我们提出了新的近端捆绑算法，以最大程度地减少非平滑凸功能。这些算法源自Nesterov快速梯度方法的应用，以使凸的平滑凸量最小化至所谓的Moreau-Yosida正则化$f_μ$ f $ f $ w.r.t.一些$μ> 0 $。由于难以评估$f_μ$的确切值和梯度，因此由于捆绑策略，我们使用近似近端点来获得可实现的算法。这些算法之一似乎是惯性近端算法的特殊情况的可实施版本。我们根据原始函数值给出了它们的复杂性估计，并报告一些初步的数值结果。
We propose new proximal bundle algorithms for minimizing a nonsmooth convex function. These algorithms are derived from the application of Nesterov fast gradient methods for smooth convex minimization to the so-called Moreau-Yosida regularization $F_μ$ of $f$ w.r.t. some $μ>0$. Since the exact values and gradients of $F_μ$ are difficult to evaluate, we use approximate proximal points thanks to a bundle strategy to get implementable algorithms. One of these algorithms appears as an implementable version of a special case of inertial proximal algorithm. We give their complexity estimates in terms of the original function values, and report some preliminary numerical results.
