An elementary proof is given of a sufficient optimality condition recently proven by B.D. Craven. This proof avoids the use of a transposition theorem and this allows for a strengthening of Craven's result. Recently Craven [2] has given a general sufficiency theorem for a Fritz John necessary condition [6] to imply optimality. This extended a sufficiency result for complex programmes given by Gulati [5] which was in turn stimulated by necessary conditions proved by Craven and Mond [3], [4]. It

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... s the purpose of this note to correct an omission in the statements of the theorems in [2] and [5] and to provide a simpler proof of a more general result than in [2]. Our notation is as in [2] . Consider