How the rho setting impacts the result?

[yeasmin62]

Hi,

I have gone through the similar discussions about the rho setting. However, I am still confused about the result I am getting for my problem setting.

I am working with some problem containing 8157constraints and 2575 variables. I am randomly generating one subproblem and then using the result of this subproblem to warm start the whole problem.

My osqp serup is
adaptive-rho-interval =10
Adaptive-rho-tolerance=1
Scaling = True
and I tried the rho values for 0.1, 0.01, 0.001, 0.0001, 0.00001. Other parameters are default.
rho percentage of correct results
0.1 4.1
0.01 9.55
0.001 39.7
0.0001 52.26

smaller rho values are giving more correct results.

Could you please help me saying what could happen and what can I interpret from this rho setting?

To my understanding, smaller rho values focuses on minimizing the objective funtion and larger rho values focuses on satisfying the constraints. but in my case smaller rho is giving more correct results.