Nonlinear Functional Versions of the Neyman–Pearson Lemma

Versions of the Neyman–Pearson lemma are given (Theorems 1 and 2) which provide sufficiency criteria for constrained extrema of nonlinear functionals with continuous or discrete variation. The use of ratio contours is described as a technique for producing a trial solution to be tested against Theorem 1 or 2. Examples of applications include improvements over previously published methods of solutions of certain problems. Relationship to previous versions of the lemma and to the method of Lagrange multipliers is discussed.