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A primal-dual integral method in global optimization

100%

Hichert J., Hoffmann A., Phú H., Reinhardt R.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2000

tom 20

nr 2

257-278

Using the Fenchel conjugate $F^c$ of Phú's Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.

A level set method in shape and topology optimization for variational inequalities

100%

Fulmański P., Laurain A., Scheid J.-F., Sokołowski J.

International Journal of Applied Mathematics and Computer Science

2007

tom 17

nr 3

413-430

The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 International Journal of Applied Mathematics and Computer Science

1 Fulmański P.

1 Hichert J.

1 Hoffmann A.

1 Laurain A.

1 Phú H.

1 Reinhardt R.

1 Scheid J.-F.

1 Sokołowski J.

1 2007

1 2000

Wyniki wyszukiwania

A primal-dual integral method in global optimization

A level set method in shape and topology optimization for variational inequalities