Solution to a Class of Optimization Problems with Amplitude Constraints

Let
H[s(\bullet),t]
be a functional of the function
s(\bullet)
and the independent variable
t
. The criterion functional
J(s)
is defined to be the integral of
H
over
T
, a set of points
t
. The problem considered is the maximization of
J(s)
with respect to an amplitudeconstrained function
s
. Necessary conditons for the optimal solution are obtained, and a method of determining the optimum
s
is given. Some examples are presented to clarify the theorems and their applications.