Let C be a convex set in Rn, and let f be a differentiable function on an open set containing C .
First-order necessary condition for a local minimizer : If x∗ ∈ C
is a local minimizer of f on C, then the inner product <∇f(x∗), x − x∗> ≥ 0 for all x ∈ C.
I cannot understand the last line of the proof , how does it take the inner product?
