An omission in growth theory concerns the existence of optimal programs in models that simultaneously include non-stationary non-convex technologies, non-convex preferences, multisectors and undiscounted utility sums. Non-stationarities rule out the classical route employing golden rule programs; non-convexities vitiate classical duality methods based on separating hyperplane theorems; multisectors destroy the regularity in the dynamics of the one-sector growth model; and divergent utility sums render inapplicable the Weierstrass approach based on compactness-continuity arguments. This paper proves the existence of optimal programs in such generally specified models, by utilizing the non-convex duality theory of Balder to replace the bilinear functional that links a topological dual pair by a class of non-linear functions that are of needle type at the origin of the commodity space.