X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/desynchronisation-controle.git/blobdiff_plain/ae93ee0d91e2a8f31ec45f7b77f9e81294630f07..fe438aa764b5d1ad7ea61512cffbb3761eff99b7:/IWCMC14/convexity.tex?ds=sidebyside

diff --git a/IWCMC14/convexity.tex b/IWCMC14/convexity.tex
index 172ca37..ff4656d 100644
--- a/IWCMC14/convexity.tex
+++ b/IWCMC14/convexity.tex
@@ -46,4 +46,27 @@ Provided $p^{5/3}$ is replaced by $P$, we have a quadratic function
 which is strictly convex, for any value of $\lambda_h$ since the discriminant 
 is positive. 
 
-  
\ No newline at end of file
+This proposed enhacement has been evaluated as follows:  
+10 tresholds $t$, 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 treshold with 
+the two approaches: either the original one ore the
+one which is convex garantee.
+
+The Figure~\ref{Fig:convex} summarizes the average number of convergence 
+iterations for each tresholdvalue. As we can see, even if this new 
+enhanced method introduces new calculus, 
+it only slows few down the algorithm and garantee the convexity, 
+and thus the convergence.
+
+\begin{figure*}
+\begin{center}
+\includegraphics[scale=0.5]{convex.png}
+\end{center}
+\caption{Original Vs Convex Garantee Approaches}\label{Fig:convex}
+\end{figure*} 
+
+
