Trust region methods with hierarchical finite element models for PDE-constrained optimization
Trust region methods with hierarchical finite element models for PDE-constrained optimization
复制标题
用于 PDE 约束优化的分层有限元模型的信赖域方法
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
B. Vexler
中科院分区：
文献类型：
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作者：
Alana Kirchner;Dominik Meidner;B. Vexler
：在本文中，开发了一种用于解决 PDE 约束优化问题的分层信任域算法。有限元网格的层次结构用于定义二次模型的层次结构，以逼近最精细网格上的离散降低成本函数。该算法同时控制模型的选择和信任区域半径的大小。信赖域收敛理论的应用可以证明算法产生的序列的每个累积点都是离散问题的驻点。数值示例说明了该方法的行为，并显示与标准牛顿信赖域方案相比，计算时间大大减少。
: In this paper, a Hierarchical Trust Region Algorithm for solving PDE-constrained optimization problems is developed. A hierarchy of finite element meshes is used to define a hierarchy of quadratic models for the approximation of the discrete reduced cost functional on the finest mesh. The proposed algorithm simultaneously controls the choice of the model and the size of the trust region radius. Application of the trust region convergence theory allows for proving that every accumulation point of the sequence produced by the algorithm is a stationary point of the discretized problem. Numerical examples illustrate the behavior of the method and show a considerable reduction of computation time compared to the standard Newton trust region scheme.