论文标题
通过修改的增强拉格朗日方法解决不一致的约束问题的问题
Solving Problems with Inconsistent Constraints with a Modified Augmented Lagrangian Method
论文作者
论文摘要
我们提出了一种数值方法，用于最大程度地减少约束优化问题，其中将目标增加，并以不一致的平等约束对二次惩罚。这些目标是由直接转录最佳控制问题的二次积分惩罚方法引起的。与二次罚款方法（QPM）相比，增强拉格朗日方法（ALM）具有许多优势。但是，如果平等约束不一致，则ALM可能不会收敛到最小化目标和罚款术语的偏见的程度。因此，我们提出了适合我们目的的ALM的修改。我们证明了修改方法的收敛性，并通过未修改方法的局部收敛率限制了其局部收敛率。数值实验表明，修改后的ALM可以比QPM快地最小化某些二次惩罚功能，而未修改的ALM收敛到一个明显不同的问题的最小化器。
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM). However, if the equality constraints are inconsistent, then ALM might not converge to a point that minimizes the bias of the objective and penalty term. Therefore, we present a modification of ALM that fits our purpose. We prove convergence of the modified method and bound its local convergence rate by that of the unmodified method. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem.
