In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph is a convex set. In simple terms, a convex function graph is shaped like a cup , while a concave function's graph is shaped like a cap .

Claude Lemaréchal is a French applied mathematician, and former senior researcher at INRIA near Grenoble, France.