LMIs: Ellipsoid containing other ellipsoids/polyhedra, Yalmip/Sedumi/Matlab (2): minimum area

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 09:39

Summary:

This video is a continuation of the video [lmielout1EN]. In said video, the LMI restrictions were proposed so that an ellipse included a polyhedron and another given ellipse. Then the radius of the circumscribed circumference of said ellipse was minimized, thereby minimizing the semimajor axis of the searched ellipse.

In this video it is discussed that, since the minor axis of the result is not unique, you can try to minimize it with 10,000 times less “force”... adding 1e-4 times the trace of the matrix to the objective function, you get something similar to the ellipse with “minimum minor axis” among the many ellipses with “minimum major axis” feasible as an optimal solution to the problem we are considering.

The second part of the video discusses how to truly obtain the minimum area ellipse, using the Yalmip geomean command. This would obtain the minimum-volume ellipsoid in three or more dimensions.

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