In your experience, what were the dimensions of the matrix you were using for a “big” problem that cvx could not solve?
That is really difficult to answer.
It depends on which solver you use with CVX, what class of problem (LP, SDP, ILP, …),
and even on the nature of the specific problems.
You can solve really large sparse conic problems with some the commercially supported solvers, but a moderately small integer problem can turn out to be very difficult.
That said, here a typical numbers that should be in the comfort zone of CVX and the underlying solvers:
- Sparse LP and SOCPs, up to 10.000 constraints and 100.000 variables (stress on
sparsity). The modeling overhead is likely to be quite substantial for large sparse problems, and may be much larger than the solution time.
- SDP, a few SDP variables of dimension up to 1000.
I’ve received reports of problems being successfully solved with CVX with over a million variables, but they were SOCPs, the computer being used had quite a bit of memory, and the solver was quite slow…