Bergounioux, Maïtine; Tiba, Dan Optimal control for the obstacle problem with state constraints. (English) Zbl 0914.49010 ESAIM, Proc. 4, 7-19 (1998). 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) Cited in 1 Document MSC: 49K20 Optimality conditions for problems involving partial differential equations 49M29 Numerical methods involving duality Keywords:constrained control problems; variational inequalities; optimality conditions; optimal control; elliptic variational inequality; necessary optimality conditions; constraints PDFBibTeX XMLCite \textit{M. Bergounioux} and \textit{D. Tiba}, ESAIM, Proc. 4, 7--19 (1998; Zbl 0914.49010) Full Text: DOI