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Feature/lower bounds #567

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@aidanproy aidanproy commented Dec 9, 2019

Add lower bounds for the energy of BinaryQuadraticModels.

This code adds two lower bounds: one based on a linear programming relaxation, the other based on a semidefinite programming relaxation. Mathematical details are provided in the code comments.

The LP relaxation uses the python package "mip" and the SDP relaxation uses scipy. However I haven't modified requirements.txt or setup.py, as I'm not sure of the best way to handle these dependencies. The mip package requires python >3.5, so I assume the lower bounds should only be installed optionally. I'd appreciate feedback on this.

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