This paper analyzes the approximate augmented Lagrangian dynamical systems for constrained optimization. We formulate the differential systems based on first derivatives and second derivatives of the approximate augmented Lagrangian. The solution of the original optimization problems can be obtained at the equilibrium point of the differential equation systems, which lead the dynamic trajectory into the feasible region. Under suitable conditions, the asymptotic stability of the differential systems and local convergence properties of their Euler discrete schemes are analyzed, including the locally quadratic convergence rate of the discrete sequence for the second derivatives based differential system. The transient behavior of the differential equation systems is simulated and the validity of the approach is verified with numerical experiments.

中文翻译：

---

基于近似增广拉格朗日方程的非线性规划微分方程方法。

本文分析了约束优化的近似增广拉格朗日动力系统。我们根据近似增强拉格朗日方程的一阶导数和二阶导数来制定微分系统。原始最优化问题的解可以在微分方程系统的平衡点获得，这将动态轨迹引导到可行区域。在适当的条件下，分析了微分系统的渐近稳定性及其Euler离散方案的局部收敛性，包括基于二阶导数的差分系统离散序列的局部二次收敛率。仿真了微分方程系统的暂态行为，并通过数值实验验证了该方法的有效性。