[Feature Request] Customised Error for infeasible problem

[Waschenbacher]

🚀 Feature Request

Replace the general ValueError with a custom error, when infeasible point is found.

Motivation

We are calling the get_polytope_samples() function and would like to catch the error caused by infeasibility. Currently, infeasible case would raise a ValueError, see the code snippet below from find_interior_point()

    if result.status == 2:
        raise ValueError(
            "No feasible point found. Constraint polytope appears empty. "
            + "Check your constraints."
        )
    elif result.status > 0:
        raise ValueError(
            "Problem checking constraint specification. "
            + f"linprog status: {result.message}"
        )

To differentiate ValueErrors arising from various causes, it would be beneficial to assign a specific custom error, such as InfeasibleProblemError, for scenarios where no feasible point is found.

[Balandat]

That makes a lot of sense; I'd be happy to include such a change. Would you be willing to put up a PR for this?

There are probably a few other places where we could use such an error, e.g. here and here.