Match infeasible problem handling to CVXPY

[TimWalter]

Hey,
Noticing that the current behaviour for an infeasible problem in the batch is just to throw a SolverError.

I think matching the CVXPY interface of just reporting infeasibility would be advantageous because

• it matches the CVXPY behaviour
• it allows using DiffCP and CVXPYLayers for feasibility problems, which is currently cumbersome

I assume this would require some work, since its has to be kept track of, which thread is dealing with an infeasible problem and there would be a need for additional returns. Moreover, it probably makes no sense to support this for solve_and_derivative_batch but only for solve_only_batch.

However given the desire to fulfill cvxpy/cvxpy#2485, this may be required eventually anyway.

[PTNobel]

We could maybe add a flag to write nan instead of raising an error. I can see how the nonderivative batch application would be quite useful with feasibility problems.

[TimWalter]

That could be an option and would resemble the status problem flag in CVXPY?
For this to be useful however it should maybe just set the relevant variables to nan? Such that the infeasible part of the batch can be identified and the feasible part can still be used.

[PTNobel]

For this to be useful however it should maybe just set the relevant variables to nan?

Yes, exactly what I'm picturing.

And the objective would have to be either -inf/+inf to indicate infeasiable or unbounded.