A Gradient Inequality for a Class of Nondifferentiable Functions

A well known gradient inequality for differentiable convex minimands and their minima over convex sets is discussed. An analogous type of result is obtained for the class of non-differentiable convex functions of the form f(x) = a^tx + (x^tCx)^1/2 over convex polyhedral sets K = {x∣Ax ≤ b} in Euclidean n-space.