A subgradient of a concave function θ(u) at u = u∗ (where u is a row vector) is a vector ξ such that θ(u)−θ(u∗) ≤ (u−u∗)ξ for all u. Show that if θ(u∗) = f(x∗) − u∗g(x∗) for the Lagrangean function...

A subgradient of a concave function θ(u) at u = u∗ (where u is a row

vector) is a vector ξ such that θ(u)−θ(u∗) ≤ (u−u∗)ξ for all u. Show that if

θ(u∗) = f(x∗) − u∗g(x∗) for the Lagrangean function θ(u), then ξ = −g(x∗)

is a subgradient of θ(u) at u = u∗.