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2011

Projection Onto A Simplex

Chen, Yunmei, Ye, Xiaojing

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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.

Projection Onto A Simplex · Around

Built on

Proximité et dualité dans un espace hilbertien
J. Moreau · 1965
Earlier work this paper cites.
A finite algorithm for finding the projection of a point onto the canonical simiplex of ℝ n \mathbb{R}^{n}
C. Michelot · 1986
Earlier work this paper cites.

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