Semidefinite programming for optimizing convex bodies under width constraints

Terence Bayen (1) , Didier Henrion (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

We consider the problem of minimizing a functional (like the area, perimeter, surface) within the class of convex bodies whose support functions are trigonometric polynomials. The convexity constraint is transformed via the Fejer-Riesz theorem on positive trigonometric polynomials into a semidefinite programming problem. Several problems such as the minimization of the area in the class of constant width planar bodies, rotors and space bodies of revolution are revisited. The approach seems promising to investigate more difficult optimization problems in the class of three-dimensional convex bodies.

Mots clés: Semi-definite programming; Support function; Convexity; Optimization

Domaines: Optimisation et contrôle [math.OC]

Terence Bayen, Didier Henrion. Semidefinite programming for optimizing convex bodies under width constraints. Optimization Methods and Software, 2012, 27 (6), pp.1073-1099. ⟨10.1080/10556788.2010.547580⟩. ⟨hal-00495031⟩