WIAS Preprint No. 1503, (2010)

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.

Appeared in

  • Ann. Acad. Rom. Sci. Math. Appl., 2 (2010) pp. 222--246.

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