A weak qualification is given which insures that a broad class of constrained optimization problems satisfies the analogue of the Kuhn-Tucker conditions at optimality. The qualification is shown to be necessary and sufficient for these conditions to be valid for any objective function which is differentiable at the optimum.

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This paper considers an N period production planning problem in which a sequence of known demands d 1, d 2,..., d N must be satisfied. The cost of production in period t consists of a setup cost K t plus a marginal cost per unit c t. The cost of carrying a unit of inventory into period t is h t - 1 . An optimal policy is a production plan that satisfies demand at minimum cost. The main results of the paper are a theorem that decreases the computational effort required to find optimal policies and a theorem that establishes the existence of planning horizons. The results of these two theorems are combined in a forward algorithm for the efficient solution of the problem.

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This paper establishes necessary and sufficient conditions for constraint set stability requiring neither convex constraint functions not convex constraint sets. These conditions then lead to a sufficiency result for the continuity of the optimal objective values as the right-hand side varies. Applications to quasiconvex functions are presented.