论文标题
一种通用加速偶对偶对凸优化问题的方法
A universal accelerated primal-dual method for convex optimization problems
论文作者
论文摘要
这项工作提出了一种通用加速的一阶原始偶对偶，用于受约束的凸优化问题。它可以处理Lipschitz和Hölder梯度，但不需要知道目标函数的平滑度。在线搜索部分中，它使用动态减少参数，并以中等幅度产生近似Lipschitz常数。此外，基于适当的离散lyapunov函数和某些差异/差异不等式的紧密衰减估计值，建立了通用最佳的混合型收敛速率。提供了一些数值测试以确认所提出方法的效率。
This work presents a universal accelerated first-order 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.
