A Gradient Inequality for a Class of Nondifferentiable Functions

Abstract

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 t x + ( x t Cx ) 1/2 over convex polyhedral sets K = { x ∣ Ax ≤ b } in Euclidean n -space.