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SUJET : Optimisation non-convexe
RÉSUMÉ : We present a mathematical programming model for the problem of covering solids by spheres of different radii.
Given a set of spheres, possibly with different diameters, and a solid, the goal is to locate the spheres in such a way their union forms a coverage for this solid, using the smallest possible number of spheres of this set.
This problem has an application in the radio-surgical treatment planning known as Gamma Knife and can be formulated as a non-convex optimization problem with quadratic constraints and a linear objective function.