发表机构
Chongqing Technology and Business University; Sichuan University; Sunway University（重庆工商大学; 四川大学; 双威大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对带线性等式约束的强凸优化问题，提出带隐式海森驱动阻尼的惯性原始-对偶动力学，推导对应的离散算法，证明其收敛速率与连续系统一致，还扩展到非光滑情形并通过数值实验验证。
AI 中文摘要
本文研究带有隐式海森驱动阻尼的惯性原始-对偶动力学，针对带线性等式约束的强凸优化问题展开。我们首先为目标函数值误差、可行性测度、轨迹及其对应速度向量建立快速收敛速率。通过适当调整参数，证明所提系统可达到指数收敛速率。对该动力学系统进行隐式时间离散化，推导得到用于求解强凸优化问题的惯性加速原始-对偶算法。基于李雅普诺夫方法，证明该算法的收敛速率与其连续时间对应系统一致。我们还将所得结果扩展到非光滑凸优化情形，并开展数值实验以验证理论结果。
英文摘要
This paper investigates inertial primal-dual dynamics with implicit Hessian-driven damping for strongly convex optimization problems with linear equality constraints. We first establish fast convergence rates for the objective function value error, the feasibility measure, and both the trajectory and its corresponding velocity vector. By appropriately adjusting parameters, we show that the proposed system achieves exponential convergence rates. Through implicit time discretization of the dynamical system, we derive an inertial accelerated primal-dual algorithm for solving the strongly convex optimization problems. Using Lyapunov-based method, we show that the proposed algorithm achieves convergence rates consistent with those of its continuous-time counterpart. We also extend the obtained results to non-smooth convex optimization case. Furthermore, we conduct numerical experiments to illustrate theoretical results.
