\end{table*}
-This improvment has been evaluated on a set of experiments.
-For 10 tresholds $t$, such that $1E-5 \le t \le 1E-3$, we have
-executed 10 times the aproach detailled before either with the new
+This improvement has been evaluated on a set of experiments.
+For 10 thresholds $t$, such that $1E-5 \le t \le 1E-3$, we have
+executed 10 times the approach detailed before either with the new
gradient calculus or with the original argmin one.
The Table~\ref{Table:argmin:time} summarizes the averages of these
-excution times, given in seconds. We remark time spent with the gradient
+execution times, given in seconds. We remark time spent with the gradient
approach is about 37 times smaller than the one of the argmin one.
-Among implementations of argmin aproaches, we have retained
+Among implementations of argmin approaches, we have retained
the COBYLA one since it does not require any gradient to be executed.
\begin{table*}
$$
\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
-\textrm{Convergence Treshold} &
+\textrm{Convergence Threshold} &
10^{-5} &
1.67.10^{-5} &
2.78.10^{-5} &
