Hypergraph Optimization Problems: Why is the Objective Function Linear?

Choosing an objective function for an optimization problem is amodeling issue and there is no a-priori reason that the objective functionmust be linear. Still, it seems that linear 0-1 programming formulationsare overwhelmingly used as models for optimization problemsover discrete structures. We show that this is not an accident. Undersome reasonable conditions (from the modeling point of view), thelinear objective function is the only possible one