Sufficient optimality conditions for the Moreau--Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints
- Krumbiegel, Klaus
- Neitzel, Ira
- Rösch, Arnd
2010 Mathematics Subject Classification
- 49K20 49M29
- Optimal control, semilinear elliptic equation, state constraints, regularization, Moreau--Yosida approximation, virtual control, sufficient optimality conditions
We develop sufficient optimality conditions for a Moreau-Yosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept, for which standard second order sufficient conditions have been shown. Moreover, we compare both regularization approaches within a numerical example.
- Ann. Acad. Rom. Sci. Math. Appl., 2 (2010) pp. 222--246.