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Shape optimization under width constraint. (English) Zbl 1262.65072

Summary: We introduce new numerical methods to solve optimization problems among convex bodies which satisfy standard width geometrical constraints. We describe two different numerical approaches to handle width equality and width inequality constraints. To illustrate the efficiency of our method, our algorithms are used to approximate optimal solutions of Meissner’s problem and to confirm two conjectures of E. Heil [“Kleinste konvexe Körper gegebener Dicke”, Techn. Hochschule Darmstadt 453 (1978)].

MSC:

65K10 Numerical optimization and variational techniques
49Q10 Optimization of shapes other than minimal surfaces
49M25 Discrete approximations in optimal control

Software:

LANCELOT; GALAHAD
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Full Text: DOI

References:

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