query: The Proximal Operator of the $ {L}_{1} $ Norm Function
positive_passages.docid: 21014
positive_passages.text: $ {L}_{1} $ Regularized Unconstrained Optimization Problem
negative_passages.docid: 73254
negative_passages.text: spectral radius in normed space is subadditive.
negative_passages.docid: 118564
negative_passages.text: Dual cone of a $L^1$ norm cone?
negative_passages.docid: 144382
negative_passages.text: Proving $\lVert x \rVert_3$ is smaller than euclidean norm
negative_passages.docid: 22689
negative_passages.text: Reference for trace/norm inequality
negative_passages.docid: 84448
negative_passages.text: Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $
negative_passages.docid: 30423
negative_passages.text: interior points and convexity
negative_passages.docid: 66084
negative_passages.text: Prove 1-Norm is a Norm
negative_passages.docid: 152196
negative_passages.text: About inner products, norms and metrics
negative_passages.docid: 91750
negative_passages.text: $l^p$ not norm, $p<1$
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 34272
negative_passages.text: Proving definition of norms induced by vector norms
negative_passages.docid: 106596
negative_passages.text: Why L1 norm for sparse models
negative_passages.docid: 61931
negative_passages.text: Positive operator is bounded
negative_passages.docid: 52791
negative_passages.text: Invertibility of an operator $T$ if $\|I-T\|<1$
negative_passages.docid: 23231
negative_passages.text: Convergence of $A_nT$ to $AT$ in operator norm for compact $T$
negative_passages.docid: 77493
negative_passages.text: Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$