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Equivalence of saddle-points and optima for non-concave programmes. (English) Zbl 0571.90078

A basic result of optimization 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 generalizes the class of geometric programmes.

MSC:

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
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