A Necessary and SuÆcient Optimality Condition for a Class of Nonconvex Scalar Variational Problems
Guillaume Carlier · 2004
Let us first recall some basic facts about convex functions and set some notations. First, we recall that a convex function u : [0, 1] → R is right and left-differentiable at any t ∈ (0, 1) and that it is differentiable except perhaps on an at most countable subset of (0, 1). In what follows we shall denote by U u(t+) (respectively U u(t−)) the right (respectively left) derivative of u at t ∈ [0, 1) (respectively t ∈ (0, 1]) with the convention that U u(0+)