Let F1,..., Fm+1 be real-valued functions defined over a space U.

A sufficient condition for u0 to maximize Fm+1 subject to Fi(u) ≤ ci(i = 1,..., m)

is that it satisfies these side conditions, that it maximizes Fm+1(u) − ki Fi(u) for some constants ki ≥ 0, and that Fi(uo) = ci for those values i for which ki > 0.