AI 中文总结
研究凸凹鞍点问题的预处理原始对偶算法，利用其光滑与非光滑结构，通过反对称预处理器建立非遍历收敛速率，考虑计算误差，经数值实验验证算法性能良好。
AI 中文摘要
我们通过文献[apidopoulos2026preconditioned]中引入的动力学方法，研究了一类用于凸凹鞍点问题的预处理原始对偶算法。所提出的框架利用了鞍点问题可能的光滑+非光滑结构，包括但不限于线性约束凸优化问题。所提出的反对称预处理器使我们能够建立非遍历收敛速率，同时考虑到方法实现中可能的计算误差。最后，我们给出数值实验以表明所提出的预处理原始对偶算法性能良好。
英文摘要
We study a family of preconditioned primal dual algorithms for convex-concave saddle point problems by the dynamics introduced in \cite{apidopoulos2026preconditioned}. The proposed framework exploits the possible smooth + nonsmooth structure of the saddle point formulation. It includes, but is not limited to, linearly constrained convex optimization problems. The proposed antisymmetric preconditioners allow us to establish non ergodic convergence rates, accounting for possible computational errors in the implementation of the method. Finally, we present numerical experiments to indicate our well performed preconditioned primal dual algorithms.
