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In this paper we study a control problem for a Kirchhoff-type equation. The method to obtain first order necessary optimality conditions is the Dubovitskii-Milyoutin formalism because the classical arguments do not work. We obtain a characterization of the optimal control by a partial differential system which is solved numerically. Mathematics Subject Classification. 47J05, 49J20, 49J22, 49K20.doi:10.1051/cocv/2016013 fatcat:zy27xpov7vbojl3unec6g5azva