半线性最优控制问题全局极小点的误差分析
Error analysis for global minima of semilinear optimal control problems
摘要：
在[1]中，我们考虑了半线性椭圆型偏微分方程的最优控制问题及其变分离散化，其中我们提供了一个条件，该条件允许判定必要的一阶条件的解是否是全局极小值。这个条件可以在离散水平上显式地评估。此外，我们证明了，如果上述条件保持一致的离散化参数的离散解序列收敛到相应的极限问题的整体解决方案。本文的工作是对文献[1]的补充，证明了离散整体解的误差估计。数值实验证实了我们的分析结果。
英文摘要：
In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions is a global minimum. This condition can be explicitly evaluated at the discrete level. Furthermore, we prove that if the above condition holds uniformly with respect to the discretization parameter the sequence of discrete solutions converges to a global solution of the corresponding limit problem. With the present work we complement our investigations of [1] in that we prove an error estimate for those discrete global solutions. Numerical experiments confirm our analytical findings.
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