I got a question relating the ADMM parameter rho.
In the osqp-paper (https://web.stanford.edu/~boyd/papers/pdf/osqp.pdf) section 5.2 Parameter Selection ‘Choosing rho’ it is stated that
My current Assumption would be:
Given the knowledge that some lines are equal constraints (given by evaluating upper & lower bounds) I would state that we a priori know a subset of constraints that will be active at the optimum solution. Assuming infinity as optimal factor for those constraints, why don’t we assign those lines a higher factor than 10³ * rho?
With that thoughts in mind there would arise 2 questions:
How is the value of 10³ as factor derived? I did some tryouts and a higher value e.g. 10⁶ (closer to infinity which would be ‘ideal’) did improve the runtime greatly. If I do not miss something here (e.g. recovery from bad intermediate solutions, …) this may hold for general purpose as well. FYI: I did not try it on some kind of benchmark problem yet.
If we detect constraints to be equal and hence set its rho to an active-value (10³) what are the reasonings behind updating them? Is the maximal ratio between rho_max and rho_min effecting the stability?
Thanks in advance for your answer.