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Article Dans Une Revue Journal of Computational Physics Année : 2008

Level set methods for optimization problems involving geometry and constraints II. Optimization over a fixed surface

Emmanuel Maitre
Fadil Santosa
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Résumé

In this work, we consider an optimization problem described on a surface. The approach is illustrated on the problem of finding a closed curve whose arclength is as small as possible while the area enclosed by the curve is fixed. This problem exemplifies a class of optimization and inverse problems that arise in diverse applications. In our approach, we assume that the surface is given parametrically. A level set formulation for the curve is developed in the surface parameter space. We show how to obtain a formal gradient for the optimization objective, and derive a gradient-type algorithm which minimizes the objective while respecting the constraint. The algorithm is a projection method which has a PDE interpretation. We demonstrate and verify the method in numerical examples.

Dates et versions

hal-00388029 , version 1 (26-05-2009)

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Emmanuel Maitre, Fadil Santosa. Level set methods for optimization problems involving geometry and constraints II. Optimization over a fixed surface. Journal of Computational Physics, 2008, 227 (22), pp.9596-9611. ⟨10.1016/j.jcp.2008.07.011⟩. ⟨hal-00388029⟩
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