n. 1. something entailed by the truth of some statement or the obtaining of some state of affairs, that is required to be true as a precondition for the latter to be true, so that if the necessary condition is false, then what it was a condition for must also be false. If P is a necessary condition for Q, Q implies P, and this relation is often expressed as `Q only if P'. Although a necessary condition may also be a sufficient condition, this is not in general true; for example, it is a necessary condition for a series to converge that the successive terms tend to zero, but this is not sufficient, as the harmonic series exemplifies. However, if P is a necessary condition of Q, then Q is a sufficient condition for P; so for example, to show that the successive terms tend to zero, it is sufficient to know that the series converges. 2. (Optimization theory) a necessary condition for an optimum point that one hopes is easy to verify, such as determination of a stationary point in unconstrained optimization, or of a Kuhn-Tucker point in constrained optimization, and that in the presence of an additional sufficient condition guarantees optimality. See Kuhn-Tucker conditions.