We introduce a filter mechanism to enforce convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows for equality-constrained quadratic programming steps to accelerate local convergence. We also include a feasibility restoration phase that allows fast detection of infeasible problems. We provide a convergence proof that shows that our algorithm converges to first-order stationary points. We provide preliminary numerical results that demonstrate the effectiveness of our proposed method.

我们介绍了一种滤波机制，可为非线性规划的增强拉格朗日方法强制收敛。与传统的增强拉格朗日方法相比，我们的方法不需要使用将一阶误差驱动为零的强制序列。取而代之的是，我们使用一个过滤器将最佳化指标驱动为零。从允许等式约束的二次编程步骤加速局部收敛的意义上说，我们的算法是灵活的。我们还包括一个可行性恢复阶段，可以快速发现不可行的问题。我们提供了一个收敛证明，表明我们的算法收敛到一阶平稳点。我们提供了初步的数值结果，证明了我们提出的方法的有效性。