Quantitative stability analysis of optimal solutions in PDE-constrained optimization

被引：9
作者：
Brandes, Kerstin
Griesse, Roland
机构：
[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math RICAM, A-4040 Linz, Austria
[2] Univ Bayreuth, Lehrstuhl Ingenieurmath, D-95440 Bayreuth, Germany
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 206卷 / 02期
关键词：
PDE-constrained optimization; parametric sensitivity analysis; stability; singular value decomposition;
D O I：
10.1016/j.cam.2006.08.038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
PDE-constrained optimization problems under the influence of perturbation parameters are considered. A quantitative stability analysis for local optimal solutions is performed. The perturbation directions of greatest impact on an observed quantity are characterized using the singular value decomposition of a certain linear operator. An efficient numerical method is proposed to compute a partial singular value decomposition for discretized problems, with an emphasis on infinite-dimensional parameter and observation spaces. Numerical examples are provided. (C) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码：908 / 926
页数：19
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