Comparative study of two fast algorithms for projecting a point to the standard simplex

We consider two algorithms for orthogonal projection of a point to the standard simplex. Although these algorithms are fundamentally different, the following fact unites them. When one of them has the maximum run time, the run time of the other is minimal. Some particular domains are presented whose points are projected by the considered algorithms in the minimum and maximum number of iterations. The correctness of the conclusions is confirmed by the numerical experiments independently implemented in the MatLab environment and the Java programming language. Ill. 11, bibliogr. 23.