Fast projection onto the simplex and the l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

295 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Parseval Networks: Improving Robustness to Adversarial Examples (2017, background): “This is a well studied problem (Michelot, 1986; Pardalos & Kovoor, 1990; Duchi et al., 2008; Condat, 2016).”
Computational Optimal Transport (2018, methodology): “17), this corresponds to computing Euclidean projection on (C1 a, C2 b) (with the extra positivity constraints), which can be solved efficiently using projection algorithms on simplices [Condat, 2015].”
Minimization Over the Nonconvex Sparsity Constraint Using A Hybrid First-order method (2021, methodology): “Under Slater’s condition and the positivity and finiteness of w I k , ( P GP ) can be effectively and efficiently solved by many algorithms with complexity O ( n ) in practice [16, 39].”
SSN: Learning Sparse Switchable Normalization via SparsestMax (2019, background): “(2) since sparsemax or the projection onto a simplex has been extensively explored (Martins andAstudillo 2016;Held et al. 1974; Bertsekas 2014; Condat 2016).”
Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms (2018, background): “The distribution has sparse support (it may assign exactly zero probability to low-scoring classes) and can be computed exactly in O(d) time (Brucker, 1984; Duchi et al., 2008; Condat, 2016).”
Hyperspectral Super-Resolution by Coupled Spectral Unmixing (2015, background): “Again the proximal operator for the simplex projection is computationally efficient, see [10].”