Lagrangian duality for a class of infinite programming problems

First-order necessary conditions of the Kuhn-Tucker type and strong duality are established for a general class of continuous time programming problems. To obtain these results a generalized Farkas' Theorem, stated in terms of convex and dual cones, is implemented in conjunction with a constraint qualification analogous to that found in finite-dimensional programming. The assumptions imposed are weaker than those needed in previous approaches to duality for this type of problem.