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Projection onto the capped simplex · Around

2015

Projection onto the capped simplex

Wang, Weiran, Lu, Canyi

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We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof.

Both the MATLAB and C++ implementations of the proposed algorithm can be downloaded at https://eng.ucmerced.edu/people/wwang5.

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Numerical Optimization
J. Nocedal and S. J. Wright · 2006
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Efficient projections onto the ℓ 1 \ell_{1} -ball for learning in high dimensions
J. Duchi, S. Shalev-Shwartz, Y. Singer, and T. Chandra · 2008
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