n. 1. anything that entails the truth of some statement or the obtaining of some state of affairs; having the latter as a consequence without any other conditions, so that if P is a sufficient condition for Q, then P implies Q, that is if P then Q is true. Although a sufficient condition may also be a necessary condition, this is not generally the case; for example, it is a sufficient condition for x to be non-negative that it be positive, but it is not necessary. However, if P is a sufficient condition for Q, then Q is a necessary condition for P. For example, it is a sufficient condition for x ≥ 4 to be composite that it be divisible by 3. 2. (Optimization theory) a condition ensuring that a previously computed solution to necessary conditions is actually optimal. Thus the first derivative test and second derivative test give sufficient conditions for a stationary point to be optimal, and convexity of the functions in a constrained minimization problem makes Kuhn-Tucker conditions sufficient.