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How to minimize l1-norm constrained by "infinity norm"

Let $A \in \mathbb{R}^{m \times n}$ and $b \in \mathbb{R}^m $. I have the following two problems: P.1. \begin{equation} \underset{x\in\mathbb{R}^n}{\text{minimize}} \| Ax-b \|_1 \\ \text{s.t. } \| x …
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