The Gradient Projection Method Using Curry’s Steplength
R. P. Phelps · SIAM Journal on Control and Optimization · 1986
It is shown that, using Curry’s steplength, the gradient projection method for finding constrained stationary points of a real valued $C^1 $ function on a closed convex subset C of Hilbert space can work for two rather different classes of convex sets: those with $C^2 $ boundary and “orthogonal polyhedra”. Both results are applications of Theorem 1, whose hypotheses require that the metric projection onto C possess directional derivatives which are continuous in a rather weak sense.