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Changed from T_j to indexing in comparison section

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This commit is contained in:
Andreas Tsouchlos 2023-04-02 01:19:18 +02:00
parent 1beb8c484e
commit c4a88363c5
1 changed files with 4 additions and 3 deletions
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7
latex/thesis/chapters/analysis_of_results.tex
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@ -87,7 +87,7 @@ return $\boldsymbol{s}$
\underbrace{\boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}}
_{\text{Likelihood}}
+ \underbrace{\sum_{j\in\mathcal{J}} g_j\left(
\boldsymbol{T}_j\tilde{\boldsymbol{c}} \right) }
\tilde{\boldsymbol{c}}_{N_c\left( j \right) } \right) }
_{\text{Constraints}} \\
\text{subject to}\hspace{5mm} &
\tilde{\boldsymbol{c}} \in \mathbb{R}^n
@ -104,8 +104,8 @@ while stopping criterion not satisfied do
\scaleto{\nu \cdot \boldsymbol{\gamma}^{\text{T}}\tilde{\boldsymbol{c}}}{8.5pt}}
\left( \boldsymbol{z} - \boldsymbol{u} \right) $
$\boldsymbol{z}_j \leftarrow \textbf{prox}_{\scaleto{g_j}{7pt}}
\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}}
+ \boldsymbol{T}_j\boldsymbol{u} \right) \hspace{5mm}\forall j\in\mathcal{J}$
\left( \tilde{\boldsymbol{c}}_{N_c\left( j \right) }
+ \boldsymbol{u}_{N_c\left( j \right) } \right) \hspace{1mm}\forall j\in\mathcal{J}$
$\boldsymbol{u} \leftarrow \boldsymbol{u}
+ \tilde{\boldsymbol{c}} - \boldsymbol{z}$
end while
@ -130,6 +130,7 @@ $\boldsymbol{\gamma}^\text{T}\tilde{\boldsymbol{c}}
\left( \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j \right)
+ \frac{\mu}{2}\sum_{j\in\mathcal{J}}
\lVert \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \boldsymbol{z}_j \rVert^2_2$}%
\todo{Explain the notation $\tilde{\boldsymbol{c}}_{N_c\left( j \right) }$}%
%
\noindent The objective functions of both problems are similar in that they
both comprise two parts: one associated to the likelihood that a given