+This proposed enhancement has been evaluated as follows:
+10 thresholds $t$, such that $1E-5 \le t \le 1E-3$, have
+been selected and for each of them,
+10 random configurations have been generated.
+For each one, we store the
+number of iterations which is sufficient to make the dual
+function variation smaller than this given threshold with
+the two approaches: either the original one ore the
+one which is convex guarantee.
+
+The Figure~\ref{Fig:convex} summarizes the average number of convergence
+iterations for each treshold value. As we can see, even if this new
+enhanced method introduces new calculus,
+it only slows few down the algorithm and guarantee the convexity,
+and thus the convergence.
+Notice that the encoding power has been arbitrarily limited to 10 W.
+\begin{figure*}
+\begin{center}
+\includegraphics[scale=0.5]{convex.png}
+\end{center}
+\caption{Original Vs Convex Guarantee Approaches}\label{Fig:convex}
+\end{figure*}
+
+
