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DDC: 510 × Subject: necessary optimality condition ×

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Now showing 1 - 3 of 3
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    Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Sprekels, Jürgen; Wu, Hao
    In this paper, we study an optimal control problem for a two-dimensional CahnHilliardDarcy system with mass sources that arises in the modeling of tumor growth. The aim is to monitor the tumor fraction in a finite time interval in such a way that both the tumor fraction, measured in terms of a tracking type cost functional, is kept under control and minimal harm is inflicted to the patient by administering the control, which could either be a drug or nutrition. We first prove that the optimal control problem admits a solution. Then we show that the control-to-state operator is Fréchet differentiable between suitable Banach spaces and derive the first-order necessary optimality conditions in terms of the adjoint variables and the usual variational inequality.
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    Formal adjoints of linear DAE operators and their role in optimal control
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker
    For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze the properties of the formal adjoints and their implications in solving linear-quadratic optimal control problems with DAE constraints.
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    Self-adjoint differential-algebraic equations
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Kunkel, Peter; Mehrmann, Volker; Scholz, Lena
    Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays.