Sufficient conditions for unique global solutions in optimal control of semilinear equations with C¹ nonlinearity

• Autorzy: Ahmad Ali Ahmad , Deckelnick Klaus , Hinze Michael
• Języki publikacji: EN

Abstrakty

EN

We consider a semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work, presented in Ahmad Ali, Deckelnick and Hinze (2016) we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by G¨unter Leugering, who raised the question whether the problem class considered in Ahmad Ali, Deckelnick and Hinze (2016) can be extended to the nonlinearity φ(s) = s|s|. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice.

Słowa kluczowe

EN

optimal control; semilinear PDE; uniqueness of global solutions

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 2
• Strony: 325--344
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Ahmad Ali Ahmad

• Technische Universität Chemnitz, Fakultät für Mathematik, 09107 Chemnitz, Germany

autor

Deckelnick Klaus

• Institut für Analysis und Numerik, Otto–von–Guericke–Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany

autor

Hinze Michael

• Mathematisches Institut, Universität Koblenz–Landau, Universitätstrasse 1, 56070 Koblenz, Germany

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).