TL;DR本文提出一个快速和简单的算法来计算在标准单纯形三角形上的投影,利用 Moreau 恒等式,我们展示了该问题本质上是一元最小化问题,目标函数是严格凸的,且连续可微。此外,研究表明,最多有 n 个候选者可以明确计算,而最小化程序是唯一一个落入正确区间的程序。
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 dif