LMI sets (3): plotting routine and applications

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 09:54

Summary:

This third video closes the introduction to LMI sets (and lifter ones). In here, details of the plotting code used in previous videos [lmisets1EN] and [lmisets2EN] is presented (it’s based on a ray-tracing idea, using YALMIP optimizer command, which is a faster pre-compiled version of optimize for repeated problems). Computation of the analytic center of an LMI set is also discussed.

The last part of the video discusses the kind of problems that can be addressed with SDP optimization software on LMI sets:

• Checking for intersection of several LMI sets (collision detection, say, in a planning problem)

• Optimization of linear functions on them (computation of tangent planes)

• Optimization of SDP-representable convex functions (as an example, the minimum distance between LMI sets; an explicit example of that is addressed in video [distlmisetEN] so it is omitted here).

Determining if one LMI set is contained into another may require, in a general case, other tools providing sufficient conditions via Sum of Squares (SOS) and Positivstellensatz multipliers; details on these extensions to LMIs is out of the scope of this introduction.

A later video with discussion on scaling, perspective cones and convex hull of LMI sets has been added, see [lmisets4EN].

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