Stability of Saddle Points Via Explicit Coderivatives of Pointwise Subdifferentials
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- 作者：Christian Clason ; Tuomo Valkonen
- 关键词：Metric regularity ; Aubin property ; Saddle points ; Fréchet coderivatives ; Integral functionals
- 刊名：Set-Valued and Variational Analysis
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：25
- 期：1
- 页码：69-112
- 全文大小：903KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Analysis; Probability Theory and Stochastic Processes;
- 出版者：Springer Netherlands
- ISSN：1877-0541
- 卷排序：25
文摘
We derive stability criteria for saddle points of a class of nonsmooth optimization problems in Hilbert spaces arising in PDE-constrained optimization, using metric regularity of infinite-dimensional set-valued mappings. A main ingredient is an explicit pointwise characterization of the regular coderivative of the subdifferential of convex integral functionals. This is applied to several stability properties for parameter identification problems for an elliptic partial differential equation with non-differentiable data fitting terms.