×

Optimal control for the obstacle problem with state constraints. (English) Zbl 0914.49010

The paper considers an optimal control problem governed by an elliptic variational inequality with the control in the right-hand side. In the first part of the paper by means of the penalization technique there are obtained necessary optimality conditions for the regularized problem \[ \int_\Omega [(y- y_0)^2+ Mu^2] dx\to\min, \]
\[ Ay= u+ f+ \xi\quad\text{in }\Omega,\quad y\in H^1_0(\Omega),\quad y\geq 0,\quad \xi\geq 0,\quad \int_\Omega y\xi dx\leq \alpha, \] where \(y\) is the state, \(u\) is the control, \(\xi\) is the supplementary control and \(\alpha>0\) is the regularization parameter. In the second part of the paper, the authors derive necessary optimality conditions (expressed in terms of subdifferentials) for the original problem \((\alpha= 0)\) with additional constraints on the state.
Reviewer: U.Raitums (Riga)

MSC:

49K20 Optimality conditions for problems involving partial differential equations
49M29 Numerical methods involving duality
PDFBibTeX XMLCite
Full Text: DOI