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## Proof

To simplify the analysis, we make two additional technical assumptions:

- The domain \( \mathcal{D} \) has nonempty interior (hence, \(\text{relint} \mathcal{D} = \text{int} \mathcal{D}\)).
- We also assume that \( A \) has full rank, i.e., \(\text{Rank } A = p\).

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A. d’Aspremont. Convex Optimization M2.  
43/49
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