原–对偶加速动力系统的稳定性分析
Stability Analysis of a Primal-Dual Accelerated Dynamical System
DOI: 10.12677/aam.2026.155206, PDF,   
作者: 曾杨洋：浙江师范大学数学科学学院，浙江 金华
关键词: 凸优化；动力系统；Lyapunov函数；Convex Optimization； Dynamical Systems； Lyapunov Function
摘要: 本文从连续时间动力系统的角度，研究一类用于线性约束凸优化问题的扰动原–对偶加速动力系统。通过构建一个同时刻画原变量与对偶变量的统一Lyapunov函数，在凸与强凸两种情形下分别推导了扰动情形下的能量衰减性与渐近收敛性。
Abstract: From the perspective of continuous-time dynamical systems, this paper studies a class of perturbed primal-dual accelerated dynamical systems for linearly constrained convex optimization problems. By introducing a unified Lyapunov function that captures both the primal and dual variables, we derive energy decay estimates and establish asymptotic convergence properties in the presence of perturbations for both convex and strongly convex cases.
文章引用：曾杨洋. 原–对偶加速动力系统的稳定性分析[J]. 应用数学进展, 2026, 15(5): 35-43. https://doi.org/10.12677/aam.2026.155206

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