论文标题
布雷格曼增强拉格朗日及其加速度
Bregman Augmented Lagrangian and Its Acceleration
论文作者
论文摘要
我们研究Bregman增强拉格朗日方法（BALM），以解决线性约束的凸问题。对于经典的增强拉格朗日方法，融合率及其与近端方法的关系得到了很好的理解。但是，在文献中尚未对香脂的收敛速率进行彻底研究。在本文中，我们根据原始目标和违反可行性分析了香脂的收敛速率。我们还首次开发了一个加速的Bregman近端方法，该方法将收敛速率从$ O（1/\ sum_ {k = 0}^{t-1}^{t-1}} $ o（1/（\ sum_ {\ sum_ {k = 0}） $ \ {η_k\} _ {k = 0}^{t-1} $是接近参数的顺序。当应用于线性约束的凸面程序的双重双重时，这会导致构建加速的脂肪，从而实现了原始和双收敛的提高。
We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood. However, the convergence rate for BALM has not yet been thoroughly studied in the literature. In this paper, we analyze the convergence rates of BALM in terms of the primal objective as well as the feasibility violation. We also develop, for the first time, an accelerated Bregman proximal point method, that improves the convergence rate from $O(1/\sum_{k=0}^{T-1}η_k)$ to $O(1/(\sum_{k=0}^{T-1}\sqrt{η_k})^2)$, where $\{η_k\}_{k=0}^{T-1}$ is the sequence of proximal parameters. When applied to the dual of linearly constrained convex programs, this leads to the construction of an accelerated BALM, that achieves the improved rates for both primal and dual convergences.
