Generalized Convexity, Generalized Monotonicity: Recent Results (Nonconvex Optimization and Its Applications) 1998th Edition by Jean-Pierre Crouzeix (Editor), Juan Enrique Martinez Legaz (Editor), Michel Volle (Editor)A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems.