How to display the optimality bounds [LBD, UBD] about eago.jl HOT 1 CLOSED

Thanks for reporting this issue! Also, thanks for the detailed description, I've got a pretty good idea of the underlying issue and the resolution should be quite easy.

A little background:
We initially had a few issues due to rounding error resulting from the larger number of intermediate calculations used when computing relaxations than auxiliary variable approaches. This usually wasn't an issue but a number of users wanted to set fairly extreme tolerances. So we added a small tolerance to the upper bound (scaled an order of magnitude below the specified relative and absolute optimality tolerances to avoid spurious results). We never adjusted the algorithm to store the true value rather than this adjusted value. So EAGO should currently furnish the correct optimal point (but not the value corresponding to it). I'll push out a patch to EAGO to fix this in the next day or so.   

The console printing controls currently should allow you to inspect the solution quality (set by keyword arguments):

• verbosity::Int - Print level (0 nothing, to 4 detailed info on each node). Unless you want node specific info (primal status, termination status, etc, stick to 1).
• output_iterations::Int - Print summary statistics at every output_interations times (Iteration #, Nodes, Lower Bound, Upper Bound, Gap, Ratio, Time, Time Left)
• header_iterations::Int- how often to print the header | Iteration # | Nodes | Lower Bound | Upper Bound | Gap | Ratio | Time | Time Left | to console

I'll also give some thought on how to report the lower bound in the final console output. That said, if the final solution is OPTIMAL it will satisfy a either a relative or absolute tolerance that are set by the following keyword arguments:

• absolute_tolerance::Float64 (default = 1E-3) 
• relative_tolerance::Float64(default = 1E-3)

from eago.jl.