On semidefinite representations of plane quartics

Didier Henrion (1, 2)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 FEL CTU - Faculty of Electrical Engineering [Prague]

Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact semidefinite representation with 2 lifting variables can be obtained. Various numerical examples illustrate the techniques and suggest further research directions.

Mots clés: polynomials; algebraic geometry; semidefinite programming

Domaines: Optimisation et contrôle [math.OC]

Didier Henrion. On semidefinite representations of plane quartics. 2008. ⟨hal-00320368v1⟩