X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/desynchronisation-controle.git/blobdiff_plain/ee130e6966e1e2f76dbf655947b04762008e12b9..e02082ad2d87032e8cff4fa8cc48682c85efc624:/IWCMC14/convexity.tex?ds=sidebyside

diff --git a/IWCMC14/convexity.tex b/IWCMC14/convexity.tex
index b1f2900..de0ddbc 100644
--- a/IWCMC14/convexity.tex
+++ b/IWCMC14/convexity.tex
@@ -20,9 +20,9 @@ in equation~(\ref{eq:obj2}) by
 \delta_x \sum_{h \in V, l \in L } x_{hl}^2 
 + \delta_r\sum_{h \in V }R_{h}^2
 + \delta_p\sum_{h \in V }P_{sh}^{\frac{8}{3}}.
-\label{eq:obj2}
+\label{eq:obj2p}
 \end{equation}
-In this equation we have first introduced new regularisation factors
+In this equation we have first introduced new regularization factors
 (namely $\delta_x$, $\delta_r$, and $\delta_p$)
 instead of the sole $\delta$.  
 This allows to  further separately study the influence of each factor.
@@ -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 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*} 
+
+