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Fast Projection onto the Simplex and the l1 Ball

Abstract : A new algorithm is proposed to project, exactly and in finite time, a vector of arbitrary size onto a simplex or an l1-norm ball. It can be viewed as a Gauss-Seidel-like variant of Michelot’s variable fixing algorithm; that is, the threshold used to fix the variables is updated after each element is read, instead of waiting for a full reading pass over the list of non-fixed elements. This algorithm is empirically demonstrated to be faster than existing methods.
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Contributor : Laurent Condat <>
Submitted on : Tuesday, September 1, 2015 - 11:32:56 AM
Last modification on : Thursday, November 19, 2020 - 1:02:12 PM
Long-term archiving on: : Wednesday, December 2, 2015 - 10:21:04 AM


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Laurent Condat. Fast Projection onto the Simplex and the l1 Ball. Mathematical Programming, Series A, Springer, 2016, 158 (1), pp.575-585. ⟨10.1007/s10107-015-0946-6⟩. ⟨hal-01056171v2⟩



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