ajout comparaison convexite

[desynchronisation-controle.git] / IWCMC14 / argmin.tex

diff --git a/IWCMC14/argmin.tex b/IWCMC14/argmin.tex
index be684d45b5657674491e9625fe56d969c0c9ec6e..567785671da45be949653dce77b7549fd0dae131 100644 (file)
--- a/IWCMC14/argmin.tex
+++ b/IWCMC14/argmin.tex
@@ -47,8 +47,8 @@ v_h^{(k)}.\dfrac{\ln(\sigma^2/D_h)}{\gamma p^{2/3}} + \lambda_h^{(k)}p
 \max \left\{\epsilon,
 \left(
 \dfrac{
 \max \left\{\epsilon,
 \left(
 \dfrac{

--\lambda_h^{(k)} + \sqrt{(\lambda_h^{(k)})^2 + \dfrac{64}{9}\alpha}
-}{\frac{16}{3}\delta_p}
+-3\lambda_h^{(k)} + \sqrt{(3\lambda_h^{(k)})^2 + 64\delta_p/\gamma.\ln(\sigma^2/D_h)}
+}{16\delta_p}

 \right)^{\frac{3}{5}}
 \right\} \\
 \hline
 \right)^{\frac{3}{5}}
 \right\} \\
 \hline


@@ -89,4 +89,61 @@ $$
 \end{table*}
 
 
 \end{table*}
 
 

-This improvement 
\ No newline at end of file
+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 
+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 
+approach is about 37 times smaller than the one of the argmin one.
+Among implementations of argmin aproaches, we have retained 
+the COBYLA one since it does not require any gradient to be executed.
+
+\begin{table*}
+\begin{scriptsize}
+$$
+\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}
+\hline
+\textrm{Convergence Treshold} &
+10^{-5} &
+1.67.10^{-5} &
+2.78.10^{-5} &
+4.64.10^{-5} &
+7.74.10^{-5} &
+1.29.10^{-4} &
+2.15.10^{-4} &
+3.59.10^{-4} &
+5.99.10^{-4} &
+0.001 \\
+\hline 
+\textrm{Gradient Calculus} &
+56.29 &
+29.17 &
+37.05 &
+6.05 &
+5.47 &
+3.82 &
+1.91 &
+2.37 &
+0.87 &
+0.65 \\
+\hline
+\textrm{Argmin Method} &  
+2224.27 &
+1158.37 &
+1125.21&
+216.82&
+162.26&
+126.99&
+58.044&
+74.204&
+23.99&
+15.85\\
+\hline
+\end{array}
+$$
+\caption{Convergence Times for Gradient and Argmin Methods}\label{Table:argmin:time}
+\end{scriptsize}
+\end{table*}
+
+ 
\ No newline at end of file