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Displaying 1661 –
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This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...
An optimal control problem governed by a bilinear elliptic equation is considered. This problem is solved by the sequential quadratic programming (SQP) method in an infinite-dimensional framework. In each level of this iterative method the solution of linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is determined. Based on a POD a-posteriori error estimator developed by Tröltzsch...
An optimal control problem governed by a bilinear elliptic equation is considered. This
problem is solved by the sequential quadratic programming (SQP) method in an
infinite-dimensional framework. In each level of this iterative method the solution of
linear-quadratic subproblem is computed by a Galerkin projection using proper orthogonal
decomposition (POD). Thus, an approximate (inexact) solution of the subproblem is
determined. Based on a POD...
Clarke’s generalized derivative is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed and fixed the function is continuous and sublinear in . It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz’s product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
We prove uniformcontinuity of radiallysymmetric vector minimizers uA(x) = UA(|x|) to multiple integrals ∫BRL**(u(x), |Du(x)|) dx on a ballBR ⊂ ℝd, among the Sobolev functions u(·) in A+W01,1 (BR, ℝm), using a jointlyconvexlscL∗∗ : ℝm×ℝ → [0,∞] with L∗∗(S,·) even and superlinear. Besides such basic hypotheses, L∗∗(·,·) is assumed to satisfy also a geometrical constraint, which we call quasi − scalar; the simplest example being the biradial case L∗∗(|u(x)|,|Du(x)|). Complete liberty is given for L∗∗(S,λ)...
We describe an approach to variational problems, where the solutions appear as pointwise (finite-dimensional) minima for fixed t of the supplemented Lagrangian. The minimization is performed simultaneously with respect to the state variable x and ẋ, as opposed to Pontryagin's maximum principle, where optimization is done only with respect to the ẋ-variable. We use the idea of the equivalent problems of Carathéodory employing suitable (and simple) supplements to the original minimization problem....
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