We introduce a framework for designing primal methods under the decentralized
optimization setting where local functions are smooth and strongly convex. Our
approach consists of approximately solving a sequence of sub-problems induced
by the accelerated augmented Lagrangian method, thereby providing a systematic
way for deriving several well-known decentralized algorithms including EXTRA
arXiv:1404.6264 and SSDA arXiv:1702.08704. When coupled with accelerated
gradient descent, our framework yields a novel primal algorithm whose
convergence rate is optimal and matched by recently derived lower bounds. We
provide experimental results that demonstrate the effectiveness of the proposed
algorithm on highly ill-conditioned problems.

提出了一个在分散优化设置下设计原始方法的框架，该框架适用于局部函数光滑且强凸。通过近似解决由加速增广拉格朗日方法引起的一系列子问题，从而提供了一种演导出几个著名的分散算法的系统方法。当与加速梯度下降相结合时，我们的框架会产生一种新的原始算法，其收敛速度是最优的，并且与最近确定的下限相匹配。我们提供实验结果，证明了拟议算法在高度病态问题上的有效性。