Distance between ’LMI sets’: semidefinite programming, intersection of ellipses example SeDuMi, Yalmip.

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 06:31

Summary:

This video generalises the ideas in video [distelliEN] to computing the distance between two “LMI sets”, i.e., sets defined by the points $x\in {ℝ}^n$ such that a given $LMI(x)\succcurlyeq 0$ holds. Ellipses are LMI sets, but so are the intersection of ellipses, convex hull of ellipses, the direct sum of ellipses, polyhedra, and, in general, a class of convex shapes with polynomial boundaries (do search for works by D. Henrion from LAAS on geometry of LMI sets if you are interested in these topics).

The simplest case is computing the minimum distance between intersections of ellipsoids, so the code of the above-referred video is modified (just a couple of lines need modifications) to illustrate how LMI/SDP can handle the problem in a straightforward way (up to some numerical computation tolerances, of course).

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