Converse duality in Banach space

Two theorems on converse duality are obtained for mathematical programs in Banach spaces. The proofs are based on a Banach-space generalization of the F. John necessary condition for a constrained minimum. No use is made of Kuhn-Tucker constraint qualifications. In the second theorem, the primal program contains a nonlinear equality constraint, and a converse duality theorem is obtained, using a modified concept of convexity; this result appears new, even for finite-dimensional programs. The results are applied to a problem in optimal control.