A duality theorem for semi-infinite convex programs and their finite subprograms

In this paper, we first establish a general recession condition under which a semi-infinite convex program and its formal lagrangian dual have the same value. We go on to show that, under this condition, the following hold. First, every finite subprogram, with ‘enough’ of the given constraints, has the same value as its Lagrangian dual. Second, the weak value of the primal program is equal to the optimal value of the primal. The first draft of this work, entitled ‘Asymptotic Convex Programming’ was completed while the author was a member of the Department of Mathematical Sciences at the University of Delaware, Newark, DE 19711.