Projection onto the capped simplex
This solves a computational optimization problem for researchers and practitioners in fields like machine learning and statistics, but it is incremental as it builds on existing projection methods.
The paper tackles the problem of efficiently computing the Euclidean projection of a point onto the capped simplex, which is a simplex with uniform bounds on each coordinate, and provides a simple algorithm with implementations in MATLAB and C++.
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.