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Valider dac1b1d6 rédigé par Gwen Samain's avatar Gwen Samain
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[main.tex] Continue cites.

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\end{column}
\begin{column}{.5\linewidth}
\begin{itemize}
\item OLS\footnote{\cite{OLS}}, OMP\footnote{\cite{OMP}}, for $g(\xb) = \iota_{{\|\xb\|}_0 \leq K}$,
\item SLS\footnote{\cite{SLS}}, SBR\footnote{\cite{SBR}} for $g(\xb) = \mu {\|\xb\|}_0$,
\item OLS\footnote[frame]{\cite{OLS}}, OMP\footnote[frame]{\cite{OMP}}, for $g(\xb) = \iota_{{\|\xb\|}_0 \leq K}$,
\item SLS\footnote[frame]{\cite{SLS}}, SBR\footnote[frame]{\cite{SBR}} for $g(\xb) = \mu {\|\xb\|}_0$,
\item $\dots$
\end{itemize}
\end{column}
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\begin{column}{.5\linewidth}
$\ell_1$-norm relaxations $g(\xb) = {\|\xb\|}_1$: LASSO, solved by
\begin{itemize}
\item primal-only proximal algorithms: ISTA\footnote{\cite{Daubechies04}}, FISTA\footnote{\cite{Beck2009_FISTA}},
\item primal-dual proximal algorithms: Chambolle-Pock\foonote{\cite{Chambolle2011}}, Condat-Vu,
\item ICD\footnote{\cite{Friedman07}},
\item Active set\footnote{\cite{Lee_NIPS2006_featuresign}},
\item Homotopy\footnote{\cite{Osborne_homotopy}},
\item primal-only proximal algorithms: ISTA\footnote[frame]{\cite{Daubechies04}}, FISTA\footnote[frame]{\cite{Beck2009_FISTA}},
\item primal-dual proximal algorithms: Chambolle-Pock\footnote[frame]{\cite{Chambolle2011}}, Condat-Vu,
\item ICD\footnote[frame]{\cite{Friedman07}},
\item Active set\footnote[frame]{\cite{Lee_NIPS2006_featuresign}},
\item Homotopy\footnote[frame]{\cite{Osborne_homotopy}},
\item $\dots$
\end{itemize}
\end{column}
......@@ -549,7 +549,7 @@
\min_{\xb \in \mathbb{R}^Q} \underbrace{\highlight{pink}{\tfrac{1}{2} {\|\yb - \Av \xb\|}_2^2}}_{\text{data fidelity}} + \underbrace{\highlight{lime}{\mu {\|\xb\|}_0}}_{\text{regularizer}}
\end{equation*} $\rightarrow$ NP-hard.
Approach in this thesis: exact resolution\footnote{ref}, from the work of~\cite{Ramzi_these}, using a branch-and-bound algorithm. Such algorithm:
Approach in this thesis: exact resolution as\footnote{\cite{Ramzi_2021_art}}\footnote{\cite{Guyard_node_screening}}\footnote{\cite{Hazimeh2021SparseRA}}, using the work of\footnote{\cite{Ramzi_these}}, which developed a dedicated branch-and-bound algorithm. Such algorithm:
\begin{itemize}
\item implicitely explore all the combinatorial space,
\item is garanteed to find the global minimum of the problem in a \emph{finite} number of iterations,
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