Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems
Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems
复制标题
基于偏微分方程模型的优化问题的同时伪时间步长
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
V. Schulz
中科院分区：
文献类型：
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作者：
S. Hazra;V. Schulz
在本文中，我们提出了一种解决带有偏微分方程约束的优化问题的新方法。它基于演化方程的同时伪时间步进。新方法可以被视为连续简化 SQP 方法，因为它使用从该方法派生的预处理器。预处理器中的简化 Hessian 矩阵由伪微分算子近似，其符号可以通过分析方法进行研究。我们将我们的方法应用于边界控制模型问题。新的优化方法需要的总计算量是单独解决模拟问题的 3.2 倍。
In this paper we present a new method for the solution of optimization problems with PDE constraints. It is based on simultaneous pseudo-time stepping for evolution equations. The new method can be viewed as a continuous reduced SQP method in the sense that it uses a preconditioner derived from that method. The reduced Hessian in the preconditioner is approximated by a pseudo-differential operator, whose symbol can be investigated analytically. We apply our method to a boundary control model problem. The new optimization method needs 3.2-times the overall computational effort of the solution of simulation problem alone.