Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 53, Issue 2, Pages 874-904Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140960645
Keywords
optimal control; finite elements; semilinear elliptic PDE; state constraints; a priori error estimates
Categories
Funding
- Austrian Science Fund (FWF) [W1244] Funding Source: Austrian Science Fund (FWF)
Ask authors/readers for more resources
We study a class of semilinear elliptic optimal control problems with pointwise state constraints. The purpose of this paper is twofold. First, we present convergence results for the finite element discretization of this problem class similarly to known results with finite-dimensional control space, thus extending results that are-for control functions-only available for linear-quadratic convex problems. We rely on a quadratic growth condition for the continuous problem that follows from second order sufficient conditions. Second, we show that the second order sufficient conditions for the continuous problem transfer to its discretized version. This is of interest, for example, when considering questions of local uniqueness of solutions or the convergence of solution algorithms such as the SQP method.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available