Projection Onto A Simplex

Yunmei Chen; Xiaojing Ye

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arXiv · 1101.6081

Projection Onto A Simplex

Yunmei Chen·Xiaojing Ye

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Abstract

This mini-paper presents a fast and simple algorithm to compute the projection onto the canonical simplex $\triangle^n$. Utilizing the Moreau's identity, we show that the problem is essentially a univariate minimization and the objective function is strictly convex and continuously differentiable. Moreover, it is shown that there are at most n candidates which can be computed explicitly, and the minimizer is the only one that falls into the correct interval.

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BibTeX RIS

Yunmei Chen, Xiaojing Ye. 2011-02-10. Projection Onto A Simplex. https://arxiv.org/abs/1101.6081

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