Currently, there is no direct way to set a lower bound for a minimization objective (or an upper bound in the case of maximization) in Gurobi.
While providing an objective bound may seem like a good idea, adding the lower bound may result in dual degeneracy. Such a bound may also lead to a less productive tree path during a MIP solve, since the artificial bound may result in less effective branching and node selection heuristics.
For a more elaborate discussion and explanation, please refer to this OR-stackexchange post and this OR in an OB world post.
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