Projection Onto A Simplex

By Yunmei Chen, Xiaojing Ye. 2011

250 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Fei Wang
2. Robert Sorrentino
3. Ping Zhang
4. Jianying Hu
5. Anita M. Preininger

In Computer Graphics and Computer-Aided Design

1. Fei Wang
2. Robert Sorrentino
3. Ping Zhang
4. Jianying Hu

In Numerical Analysis

1. Fei Wang
2. Robert Sorrentino
3. Ping Zhang
4. Jianying Hu

Citations in the corpus

• Label Propagation Prediction of Drug-Drug Interactions Based on Clinical Side Effects (2015, methodology): “This is a Euclidean projection problem under the simplex constraint and can be solved by the algorithm in 27,28 (as in our experiments).”