How to choos the penalty term rho? And should we scale it?

[WJY-Mark]

ADMM is sensitive to penalty term rho, is there any law or experience about how to choose rho?
According to the paper, we pre-compute a set of matrices according to different rho. Does this mean we should update rho in every cycle(such as rho = min(rho*10, 10e8), maybe it will speed up the convergence? ), and use pre-compute corresponding Q & R & P & K... Matrices?

[plancherb1]

Unfortunately it tends to be a bit problem specific. However the OSQP paper does provide some guidance and algorithmic ways to adjust things. The challenge is that rho is baked into the cache and so updating it is challenging from a memory perspective as you'd need a set of cache values. We've done that at small scales with e.g., 3 sets of values but at some point you'll run out of memory. That said, we are actively working on a way to get around this challenge and hope to be releasing that (along with more code cleanup / documentation / bug fixes) in the next two months or so. So stay tuned! For now, you'll want to experiment around a bit for your application and find a couple of values that work well and do some discrete switches!