Maximum volume ellipsoid inside polyhedron and other ellipsoids: 2D example, Matlab (LMI/SDP)

Antonio Sala, UPV

Difficulty: ***** ,       Relevance: ,      Duration: 15:36

Summary:

This video discusses the problem of obtaining the maximum volume ellipsoid inside a convex body defined as the intersection of polyhedra and ellipsoidal sets, not centered neither symmetric with respect to the origin as in other prior videos of the collection; well, as we are detailing a 2D example, we will actually speak abput polygons and maximum area ellipse, but the ideas efficiently generalise to higher dimensions in a trivial way.

We use Matlab+YALMIP+SeDuMi to solve the associated semidefinite programming, setting linear matrix inequalities and a ‘geomean’ objective function (used by Yalmip/SeDuMi instead of ‘logdet’).

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.