Optimal Control of PDEs with Regularized Pointwise State Constraints
This paper addresses the regularization of pointwise state constraints in optimal control problems. By analyzing the associated dual problem, it is shown that the regularized problems admit Lagrange multipliers in L2-spaces. Under a certain boundedness assumption, the solution of the regularized problem converges to the one of the original state constrained problem. The results of our analysis are confirmed by numerical tests.
Keywordsquadratic programming regular Lagrange multipliers optimal control elliptic and parabolic equations pointwise state constraints bottleneck constraints
Unable to display preview. Download preview PDF.
- 4.M. Bergounioux and F. Tröltzsch, “Optimal control of linear bottleneck problems,” ESAIM, Control, Optimisation and Calculus of Variations, vol. 3, pp. 235–250,1998.Google Scholar
- 10.F. Tröltzsch, “Regular Lagrange multipliers for control problems with mixed pointwise control-state constraints,” SIAM J. Optimization, to appear.Google Scholar