A Universal Accelerated Primal–Dual Method for Convex Optimization Problems

被引：0
作者：
Hao Luo
机构：
[1] Chongqing Normal University,National Center for Applied Mathematics in Chongqing
[2] Peking University,Chongqing Research Institute of Big Data
来源：
Journal of Optimization Theory and Applications | 2024年 / 201卷
关键词：
Convex optimization; Primal–dual method; Mixed-type estimate; Optimal complexity; Bregman divergence; Lyapunov function; 65B99; 68Q25; 90C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：280 / 312
页数：32
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