A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
复制标题
椭圆 MPEC 的平滑惩罚方法和非线性多重网格算法
DOI：
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发表时间：
2011
影响因子：
2.2
通讯作者：
I. Kopacka
中科院分区：
文献类型：
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作者：
M. Hintermüller;I. Kopacka
研究了一类带双边控制约束的第一类椭圆型变分不等式最优控制问题。利用光滑罚技术证明了该变分不等式的稳定点收敛于极限问题的E-几乎C-稳定点。使用全近似多重网格法（FAS）和第二类多重网格法的收敛结果给出了解决的子问题。提供了一个整体的算法概念，并通过实例讨论了其性能。
An optimal control problem governed by an elliptic variational inequality of the first kind and bilateral control constraints is studied. A smooth penalization technique for the variational inequality is applied and convergence of stationary points of the subproblems to an E-almost C-stationary point of the limit problem is shown. The subproblems are solved using a full approximation multigrid scheme (FAS) and alternatively a multigrid method of the second kind for which a convergence result is given. An overall algorithmic concept is provided and its performance is discussed by means of examples.