Hi there,
I have a question. What choice is better for feeding a Mosek solver? 1- High number of constraints (for example 10^7) and low number of decision variables (x) (like 10), or its dual equivalent with low number of constraints (i.e. 10) and high number of decision variables (10^7)?
Is there any difference in the convergence speed?
Which of them is better in terms of MOSEK restriction (2^31 entries at each moment)?
Thanks
Fewer constraints than variables are normally better. But it is only a rule of thumb.
In fact the theoretical complexity of solving the primal and the dual is the same.
Yes, makes sense. Thanks.
And somewhere in the mix is CVX’s decision on whether to dualize.
By this you mean that CVX intervene in the performance of MOSEK solver to convert the primal problem to a dual one in some situations? If the dual one is easier to handle.
If it dualizes, CVX will output a message:
For improved efficiency, [solver name] is solving the dual problem.
prior to the solver output. I don’t know the criteria CVX uses to decide whether to do so.
