Projected gradient descent
= Projected gradient descent
For a convex set $C$ and a differentiable convex objective $F$, projected gradient descent uses
$$
x_{i+1}=\Pi_C(x_i-\eta\nabla F(x_i)).
$$
This is the <proximal gradient method> when the nonsmooth term is the indicator of the feasible convex set, whose proximal operator is the metric projection.