Ordinary convex programs without a duality gap

In the Kuhn-Tucker theory of nonlinear programming, there is a close relationship between the optimal solutions to a given minimization problem and the saddlepoints of the corresponding Lagrangian function. It is shown here that, if the constraint functions and objective function arefaithfully convex in a certain broad sense and the problem has feasible solutions, then theinf sup andsup inf of the Lagrangian are necessarily equal.This work was supported in part by the Air Force Office of Scientific Research under Grant No. AF-AFOSR-1202-67B.