I have a minimization problem for which I am having some misunderstandings and confusions with regard to some results I am getting for an ILP and its LP relaxation.
In the ILP I have two decision variables, one is binary while the other is continuous. There is a bilinear term involving the product of the binary variable in the ILP. I introduced the McCormick Envelopes to eliminate the bi-linear term in the relaxed version.
What I do not understand is that after a deterministic rounding scheme I developed, the value of the cost function is less than or equal to the optimal cost function value. Is that correct ? Am I missing something somehow ?