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Existence and uniqueness of solutions of the state equation, existence of global optimal solutions, differentiability of the control-to-state map and first-order necessary optimality conditions are established. The aforementioned results require the controls to be functions in<jats:inline-formula><jats:alternatives><jats:tex-math>$$H^1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msup><mml:mi>H<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msup><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and subject to pointwise lower and upper bounds. In order to obtain the Newton differentiability of the optimality conditions, we employ a Moreau\u2013Yosida-type penalty approach to treat the control constraint and study its convergence. The first-order optimality conditions of the regularized problems are shown to be Newton differentiable, and a generalized Newton method is detailed. A discretization of the optimal control problem by piecewise linear finite elements is proposed and numerical results are presented.<\/jats:p>","DOI":"10.1007\/s10589-023-00463-6","type":"journal-article","created":{"date-parts":[[2023,3,26]],"date-time":"2023-03-26T22:14:37Z","timestamp":1679868877000},"page":"479-508","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal control of the stationary Kirchhoff equation"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2835-2249","authenticated-orcid":false,"given":"Masoumeh","family":"Hashemi","sequence":"first","affiliation":[]},{"given":"Roland","family":"Herzog","sequence":"additional","affiliation":[]},{"given":"Thomas M.","family":"Surowiec","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,3,13]]},"reference":[{"issue":"3","key":"463_CR1","doi-asserted-by":"publisher","first-page":"1276","DOI":"10.1093\/imanum\/dry034","volume":"39","author":"L Adam","year":"2018","unstructured":"Adam, L., Hinterm\u00fcller, M., Surowiec, T.M.: A semismooth Newton method with analytical path-following for the $${H}^1$$-projection onto the Gibbs simplex. 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