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A convex approach to minimal partitions. (English) Zbl 1256.49040

Summary: We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically: we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so and also discuss some situations where it fails.

MSC:

49M29 Numerical methods involving duality
49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53C38 Calibrations and calibrated geometries
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
68U10 Computing methodologies for image processing
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