Abstract Primal–dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal–dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point.

中文翻译：

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用于约束凸优化的增强原始-对偶梯度动力学的半全局指数稳定性

摘要 寻找拉格朗日函数鞍点的原始-对偶梯度动力学已被广泛用于处理约束优化问题。在现有方法的基础上，我们扩展了增强原始-对偶梯度动力学（Aug-PDGD）以结合一般凸和非线性不等式约束，并在目标函数为强凸时建立其半全局指数稳定性。我们还提供了一个强凸二次规划的例子，其中 Aug-PDGD 无法实现全局指数稳定性。数值模拟还表明，指数收敛速度可能取决于到 KKT 点的初始距离。