Primal and Dual problem in Mosek

1

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

2

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.

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3

Yes, makes sense. Thanks.

4

And somewhere in the mix is CVX’s decision on whether to dualize.

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5

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.

6

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.

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