论文标题
不平等的自适应惩罚方法限制了最小化问题
An Adaptive Penalty Method for Inequality Constrained Minimization Problems
论文作者
论文摘要
观察到原始二重性活动方法是一系列惩罚配方序列的极限。利用这个角度，我们提出了一种惩罚方法，随着迭代的残差减少，该方法会自适应地成为主动集合方法。因此，自适应惩罚方法（APM）结合了这两种方法的主要优点，即易于实施惩罚方法以及确切的不平等限制固有的不平等约束。该方案可以视为一种准牛顿法，其中使用惩罚参数近似雅各布。通过解决辅助问题，在每次迭代中选择该空间变化的参数。
The primal-dual active set method is observed to be the limit of a sequence of penalty formulations. Using this perspective, we propose a penalty method that adaptively becomes the active set method as the residual of the iterate decreases. The adaptive penalty method (APM) therewith combines the main advantages of both methods, namely the ease of implementation of penalty methods and the exact imposition of inequality constraints inherent to the active set method. The scheme can be considered a quasi-Newton method in which the Jacobian is approximated using a penalty parameter. This spatially varying parameter is chosen at each iteration by solving an auxiliary problem.
