Regularization of state-constrained elliptic optimal control problems with nonlocal radiation interface conditions
- 146 Downloads
A state-constrained optimal control problem with nonlocal radiation interface conditions arising from the modeling of crystal growth processes is considered. The problem is approximated by a Moreau-Yosida type regularization. Optimality conditions for the regularized problem are derived and the convergence of the regularized problems is shown. In the last part of the paper, some numerical results are presented.
KeywordsNonlinear optimal control Nonlocal radiation interface conditions State constraints First-order necessary conditions Second-order sufficient conditions Moreau-Yosida approximation
Unable to display preview. Download preview PDF.
- 1.Adams, R.A.: Sobolev Spaces. Academic Press, San Diego (1978) Google Scholar
- 9.Casas, E., De Los Reyes, J.C., Tröltzsch, F.: Sufficient second order optimality conditions for semilinear control problems with pointwise state constraints (2007, submitted) Google Scholar
- 13.Hintermüller, M., Kunisch, K.: Feasible and non-interior path-following in constrained minimization with low multiplier regularity. Report 01-05, Department of Mathematics and Scientific Computing, University of Graz, Heinrichstraße 36, A-8010 Graz, Austria, October 2005 Google Scholar
- 19.Konstantinov, A.: Sublimation growth of SiC. In: Harris, G. (ed.) Properties of Silicon Carbide. EMIS Datareview Series, pp. 170–203. Institution of Electrical Engineers, INSPEC, London (1995). Chap. 8.2 Google Scholar
- 21.Meyer, C.: Optimal control of semilinear elliptic equations with applications to sublimation crystal growth. Ph.D. Thesis, TU-Berlin (2006) Google Scholar
- 23.Meyer, C., Yousept, I.: State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions (2007, submitted) Google Scholar
- 24.Philip, P.: Transient numerical simulation of sublimation growth of SiC bulk single crystals. Modeling, finite volume method, results. Ph.D. Thesis, Department of Mathematics, Humboldt University of Berlin (2003) Google Scholar