convexity modification

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

diff --git a/IWCMC14/HLG.tex b/IWCMC14/HLG.tex
index 1008903395d467242536ea10436b87e2bc5be4ab..ff12b04fa9d612566bf61cd45a0eb129bcb9809d 100644 (file)
--- a/IWCMC14/HLG.tex
+++ b/IWCMC14/HLG.tex
@@ -138,10 +138,10 @@ untill the variation of the dual function is less than a given threshold.
 $v_{h}^{(k+1)}= \max\left\{0,v_{h}^{(k)} -  \theta^{(k)}.\left( R_h^{(k)} - \dfrac{\ln(\sigma^2/D_h)}{\gamma.(P_{sh}^{(k)})^{2/3}}   \right)\right\}$
 \item 
   $\begin{array}{l}
 $v_{h}^{(k+1)}= \max\left\{0,v_{h}^{(k)} -  \theta^{(k)}.\left( R_h^{(k)} - \dfrac{\ln(\sigma^2/D_h)}{\gamma.(P_{sh}^{(k)})^{2/3}}   \right)\right\}$
 \item 
   $\begin{array}{l}

-   \lambda_{i}^{(k+1)} = \lambda_{i}^{(k)} - \theta^{(k)}.\left( 
-    q^{(k)}.B_i \right.\\
+   \lambda_{i}^{(k+1)} = \max\left\{0, \lambda_{i}^{(k)} - \theta^{(k)}.\left( 
+    q^{(k)}.B_i \right. \left.\\

   \qquad\qquad\qquad -\sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl}^{(k)} \right)   \\
   \qquad\qquad\qquad -\sum_{l \in L}a_{il}^{+}.c^s_l.\left( \sum_{h \in V}x_{hl}^{(k)} \right)   \\

-  \qquad\qquad\qquad  - \left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl}^{(k)} \right) - P_{si}^{(k)}  \right)
+  \qquad\qquad\qquad  - \left.\left. \sum_{l \in L} a_{il}^{-}.c^r.\left( \sum_{h \in V}x_{hl}^{(k)} \right) - P_{si}^{(k)}  \right) \right\}

 \end{array}
 $
 
 \end{array}
 $
 


@@ -162,7 +162,7 @@ q_i^2 + q_i.
 \right)
 \right)$
 
 \right)
 \right)$
 

-\item 
+\item \label{item:psh} 

 $
 P_{sh}^{(k)} 
 =
 $
 P_{sh}^{(k)} 
 =