Projections onto the canonical simplex with additional linear inequalities.

We consider projections onto the canonical simplex with additional linear inequalities. We mention three cases in the fields of distributionally robust optimization and accuracy at the top where such projections arise. For these specific examples we write the projections as optimization problems and show that they are equivalent to finding a zero of real-valued functions. We prove that these functions are monotonic and in some cases convex. We employ optimization methods with guaranteed convergence and derive their theoretical complexity. We demonstrate that our methods have (almost) linear observed theoretical complexity.