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Boundary integral representations of second derivatives in shape optimization

100%

Eppler K.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2000

tom 20

nr 1

63-78

For a shape optimization problem second derivatives are investigated, obtained by a special approach for the description of the boundary variation and the use of a potential ansatz for the state. The natural embedding of the problem in a Banach space allows the application of a standard differential calculus in order to get second derivatives by a straight forward "repetition of differentiation". Moreover, by using boundary value characerizations for more regular data, a complete boundary integral representation of the second derivative of the objective is possible. Basing on this, one easily obtains that the second derivative contains only normal components for stationary domains, i.e. for domains, satisfying the first order necessary condition for a free optimum. Moreover, the nature of the second derivative is discussed, which is helpful for the investigation of sufficient optimality conditions.

A regularized Newton method in electrical impedance tomography using shape Hessian information

45%

Eppler K., Harbrecht H.

Control and Cybernetics

2005

tom 34

nr 1

203-225

Ograniczanie wyników

1 Control and Cybernetics

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2 Eppler K.

1 Harbrecht H.

1 2005

1 2000

Wyniki wyszukiwania

Boundary integral representations of second derivatives in shape optimization

A regularized Newton method in electrical impedance tomography using shape Hessian information