Munapo (2016, American Journal of Operations Research, http://dx.doi.org/10.4236/ajor.2016.61001) purports to have a proof that binary linear programming is solvable in polynomial time, and hence that P=NP.

Unsurprisingly, it does not really show this.

Its results are based on a convex quadratic approximation to the problem with a penalty term whose weight $ \mathcal{l}$ needs to be infinitely large for the approximation to recover the true problem.

My questions are the following:

- Is this an approximation which already existed in the literature (I rather expect it did)?
- Is this approximation useful in practice? For example, could one solve a mixed integer linear programming problem by homotopy continuation, gradually increasing the weight $ \mathcal{l}$ ?

Note: After writing this question I discovered this related question: Time Complexity of Binary Linear Programming . The related question considers a specific binary linear programming problem, but mentions the paper above.