Equivalence of saddle-points and optima for non-concave programmes

AbstractA basic result of optimisation theory is that a saddle-point of the Lagrangian is an optimum of the associated programming problem, independently of any concavity assumptions. It is also well known that under concavity assumptions the two are equivalent; i.e., an optimum is always a saddle-point. It is demonstrated that this basic equivalence of saddle-points and optima in fact holds for a much larger class of problems, which are not necessarily concave, but are equivalent to concave programmes up to a diffeomorphism. This class generalises the class of geometric programmes