-Let us first have a discussion on the stop criterion of the citted algorithm.
+Let us first have a discussion on the stop criterion of the cited algorithm.
We claim that even if the variation of the dual function is less than a given
-threeshold, this does not ensure that the lifetime has been maximized.
+threshold, this does not ensure that the lifetime has been maximized.
Minimizing a function on a multiple domain (as the dual function)
-may indeed easilly fall into a local trap because some of introduced
+may indeed easily fall into a local trap because some of introduced
variables may lead to uniformity of the output.
\begin{figure}
\label{fig:convergence:scatterplot}
\end{figure}
-Experimentations have indeed shown that even if the dual
+Experiments have indeed shown that even if the dual
function seems to be constant
(variations between two evaluations of this one is less than $10^{-5}$)
not all the $q_i$ have the same value.
The maximum amplitude rate of the sequence of $q_i$ --which is
$\frac{\max_{i \in N} q_i} {\min_{i \in N}q_i}-1$--
-is represented in $y$-coordonates
+is represented in $y$-coordinate
with respect to the
-value of the threeshold for dual function that is represented in
-$x$-coordonates.
+value of the threshold for dual function that is represented in
+$x$-coordinate.
This figure shows that a very small threshold is a necessary condition, but not
a sufficient criteria to observe convergence of $q_i$.
In the following, we consider the system are $\epsilon$-stable if both
-maximum amplitude rate and the dual function are less than a threeshold
+maximum amplitude rate and the dual function are less than a threshold
$\epsilon$.
