An interior point algorithm with inexact step computation in function space for state constrained optimal control
An interior point algorithm with inexact step computation in function space for state constrained optimal control
复制标题
状态约束最优控制函数空间不精确步长计算的内点算法
DOI：
10.1007/s00211-011-0381-4
复制
发表时间：
2011
影响因子：
2.1
通讯作者：
A. Günther
中科院分区：
文献类型：
--
作者：
A. Schiela;A. Günther
针对带状态约束的PDE约束最优控制问题，研究了函数空间中的内点法。我们的重点是构建和分析一种将牛顿路径跟踪方法与自适应网格细化相结合的算法。这是在函数空间中的非精确牛顿方法框架中完成的，其中每个牛顿步骤的离散化误差由最内层循环中的自适应网格细化控制。这允许在粗糙网格上执行大多数所需的牛顿步骤，这样总体计算时间由最后几个步骤支配。为此，我们提出了一个适合问题范数的后验误差估计。
We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.