94) Minimum Objective Value and Local Optima
Summary
Our intention was to drive the model to an optimal converged solution of at least $7600, but what you get is: Adding this constraint to a matrix that was solving to a worse value just makes it infeasible. But it is possible that some combinations of assumed values, constraints and numerical precision could generate a non-convex problem, where there is a gap or a dip in the edges of the solution space. In this case, an additional constraint on objective value could be having a real effect because it removes the non-convex bit of the problem from the feasible region. I do note that it came from a refinery where the modeller believed in the power of the minimum objective, so perhaps they regularly had such issues owing to the nature of their sales contracts. Nonetheless, even if it sometimes looks like a minimum objective value is resolving problems with local optima solutions from an SLP model, the effect is probably unspecific and could be achieved by any number of other changes.
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