bibkey: “parikhboyd2014proximal” authors: “Neal Parikh; Stephen Boyd” year: 2014 title: “Proximal Algorithms” doi: “10.1561/2400000003” claim: “The proximal operator of a multiple of the Euclidean norm is block soft-thresholding; for a point of norm above the threshold lambda the associated minimum equals lambda times the norm minus lambda squared over two, and otherwise half the squared norm.” strata_touched: [] license: “citation-only” triage: “anchor”

Proximal Algorithms

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Foundations and Trends in Optimization 1(3), 2014, pages 127-239, Section 6.5.1 (norms and their proximal operators). Used for the per-datum lower bound lambda ||x|| - lambda^2/2 of unit-atom l1 sparse coding; the fiber-law volume adds the dictionary-level equality characterization via equality in the triangle inequality.

Declared identifiers: DOI 10.1561/2400000003.