Papers › Computing the proximal operator of the ℓ₁ induced matrix norm
Computing the proximal operator of the ℓ₁ induced matrix norm
Jeremy E. Cohen
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In this short article, for any matrix X∈ℝ^(n×m) the proximity operator of two induced norms X₁ and X_∞ are derived. Although no close form expression is obtained, an algorithmic procedure is described which costs roughly 𝒪(nm). This algorithm relies on a bisection on a real parameter derived from the Karush-Kuhn-Tucker conditions, following the proof idea of the proximal operator of the max function found in Parikh(2014).
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