Projection onto a box-constrained hyperplane
= Projection onto a box-constrained hyperplane
For $C=\{x:0\leq x\leq1,\ a^Tx=b\}$, the projection of $y$ has coordinates $x_i=\min(1,\max(0,y_i-\nu a_i))$, where the scalar multiplier $\nu$ is chosen so that $a^Tx=b$. Thus the projection reduces to a continuous one-dimensional root-finding problem.