  To achieve a maximal locality in a trivial field theory, we maximize the
ultraviolet cutoff of the theory by fine tuning the infrared values of the
parameters. This optimization procedure is applied to the scalar theory in
$D+1$ dimensions ($D \geq 4$) with one extra dimension compactified on a circle
with radius $R$. The optimized, infrared values of the parameters are then
compared with the corresponding ones of the uncompactified theory in $D$
dimensions, which is assumed to be the low-energy effective theory. We find
that these values approximately agree with each other, as long as $R^{-1} \gsim
s M$ is satisfied, where $s\simeq 10,50,50, 100$ for $D=4,5,6,7$, and $M$ is a
typical scale of the $D$-dimensional theory. This result supports the
previously made claim that the maximization of the ultraviolet cutoff in an
nonrenormalizable field theory can give the theory more predictive power.
