Review Note
Last Update: 09/23/2023 03:11 PM
Current Deck: EEN100: Theory and exercises
Published
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Front
Problem (P1) and conditions on uniqueness
Back
(P1) is the convex relaxation of (P0)
\[\min_{z \in \mathbb R^n} \lVert z \rVert_1 \quad \text{s.t. } Az = y\]Let \(x\) be an arbitrary vector supported on \(\mathcal S\) such that \(Ax = y\).
Then \(x\) is the unique solution to (P1) iff \(A\) satisfies the RNP wrt \(\mathcal S\).
\[\min_{z \in \mathbb R^n} \lVert z \rVert_1 \quad \text{s.t. } Az = y\]Let \(x\) be an arbitrary vector supported on \(\mathcal S\) such that \(Ax = y\).
Then \(x\) is the unique solution to (P1) iff \(A\) satisfies the RNP wrt \(\mathcal S\).
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