[Research] Pac Man Matrices - an interesting new convex subset of stable matrices • /r/MachineLearning

Well, without further investigation I really can't say if this would be useful for the actual use-case described in the website which is system identification. You seem to be more concerned about other use cases for this result and that is fine. It may be elegant but if it excludes a good model for the system I'm actually trying to estimate, what good is a guarantee that my estimation algorithm will converge?? Also in practice I don't think I've ever seen an actual blow up but in system identification some kind of pseudo-Newton algorithm is usually the choice, not gradient descent. Typically the cost function will usually get very steep before actually blowing up due to instability which tends to keep the algorithm away from that region.