This work presents a universal accelerated primal–dual method for affinely constrained convex optimization problems. It can handle both Lipschitz and Hölder gradients but does not need to know the smoothness level of the objective function. In line search part, it uses dynamically decreasing parameters and produces approximate Lipschitz constant with moderate magnitude. In addition, based on a suitable discrete Lyapunov function and tight decay estimates of some differential/difference inequalities, a universal optimal mixed-type convergence rate is established. Some numerical tests are provided to confirm the efficiency of the proposed method.

中文翻译：

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凸优化问题的通用加速原始-对偶方法

这项工作提出了一种用于仿射约束凸优化问题的通用加速原对偶方法。它可以处理 Lipschitz 梯度和 Hölder 梯度，但不需要知道目标函数的平滑度。在线搜索部分，它使用动态递减的参数并产生中等大小的近似Lipschitz常数。此外，基于合适的离散李亚普诺夫函数和一些微分/差分不等式的紧衰减估计，建立了通用最优混合型收敛速度。提供了一些数值测试来证实所提出方法的效率。