# Fast Projection onto the Capped Simplex withApplications to Sparse Regression in Bioinformatics

@article{Ang2021FastPO, title={Fast Projection onto the Capped Simplex withApplications to Sparse Regression in Bioinformatics}, author={Andersen Man Shun Ang and Jianzhu Ma and Nianjun Liu and Kun Huang and Yijie Wang}, journal={ArXiv}, year={2021}, volume={abs/2110.08471} }

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton’s method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a much lower computational cost compared with the existing sorting-based methods proposed in the literature. We provide a theory for partial…

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