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

页码：908 / 926

页数：19

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