talk/interation2.tex

   1 \begin{enumerate}
   2 \item
   3 $q_i^{(k)} = \arg\min_{q_i>0}
   4 \left(
   5 q^2 + q.
   6 \left(
   7 \sum_{l \in L } a_{il}w_l^{(k)}-
   8 \lambda_i^{(k)}B_i
   9 \right)
  10 \right)$
  11
  12 \item
  13 $
  14 P_{sh}^{(k)}
  15 =
  16 \arg \min_{p > 0}
  17 \left(
  18 v_h^{(k)}.\dfrac{\ln(\sigma^2/D_h)}{\gamma p ^{2/3}} + \lambda_h^{(k)}p
  19 \right)
  20 $
  21
  22 \item
  23 $
  24 R_h^{(k)}
  25 =
  26 \arg \min_{r \geq 0 }
  27 \left(
  28 \delta r^2
  29 -v_h^{(k)}.r - \sum_{i \in N} u_{hi}^{(k)} \eta_{hi}
  30 \right)
  31 $
  32 \item
  33 $
  34 x_{hl}^{(k)} =
  35 \arg \min_{x \geq 0}
  36 \left(
  37 \delta.x^2 + x.
  38 \sum_{i \in N} \left(
  39 \lambda_{i}^{(k)}.(c^s_l.a_{il}^{+} +
  40 c^r. a_{il}^{-} )+
  41  u_{hi}^{(k)} a_{il}
  42 \right)
  43 \right)
  44  $
  45 \end{enumerate}