Welcome to the OPTPDE Problem Collection
Keywords: analytic solution
Global classification: linear-quadratic, convex
Functional: convex quadratic
Geometry: easy, fixed
Design: coupled via volume data
- linear elliptic operator of order 2.
- Defined on a 2-dim domain in 2-dim space
- No time dependence.
- box of order 0
Submitted on 2014-02-15 by Winnifried Wollner. Published on 2017-01-09
The solution is parametrized in the Tikhonov parameter .
The given data is chosen in a way which admits an analytic solution. This solution is rotationally symmetric.
The following optimality system for the state , the control , the adjoint state , and Lagrange multiplier , given in the strong form, characterizes the unique minimizer.
The optimal solution together with adjoint state and Lagrange multiplier for the inequality constraint are known. They are given by
S. Cherednichenko, K. Krumbiegel, and A. Rösch. Error estimates for the Lavrentiev regularization of elliptic optimal control problems. Inverse Problems, 24 (5):055003, 21, 2008. doi: 10.1088/0266-5611/24/5/055003.