A user recently reached out to MOSEK support because the solver returned an *UNKNOWN *problem/solution status on their (constrained) Least-squares problem, that was implemented in CVXPY . The solver log looked as shown in the first MOSEK log shown below.

The solution we offered was to minimize the Euclidean norm instead of the sum-of-squares. Theoretically, both models are equivalent; their optimal points are the same. But as a great man once said: in theory, theory and practice are the same. In practice, well... Take a look at the MOSEK log for the problem that minimizes the Euclidean norm (second MOSEK log)

Note the following differences between the two MOSEK logs:

- The problem status in the norm problem is primal and dual feasible and the solution status is optimal, in contrast to the least-squares problem.
- The infinity-norm of the solutions in the norm problem are smaller by nearly 5 orders of magnitude compared to the solution of the least-squares problem. This is usually a desirable trait, as explained in the debugging section of MOSEK docs
- The number of iterations taken by the norm problem is far fewer.
- The objective value of the norm problem is essentially the square root of the least-squares problem (the least-squares problem was not solved to optimality, hence the discrepancy)

*more equal than the other*.

So, at least for CVXPY-MOSEK users (and MOSEK Fusion users!), we recommend the Euclidean norm in place of the sum-of-squares, wherever possible.