In earlier results by Sposito and David, Kuhn-Tucker type duality associated with a certain saddlepoint problem was established over convex cone domains (not necessarily polyhedral) without differentiability. Recent variants have established necessary optimality conditions of the Fritz John and Kuhn-Tucker type for programming problems over" convex polyhedral cone domains which require differentiability assumptions. This paper extends the present results in the literature to programming problems over arbitrary convex cone domains (not necessarily polyhedral).