In machine learning, the best parameters for a model are chosen so as to minimize the training objective. Strictly convex functions are paticularly interesting because they have a unique global minimum. Furthermore, for strict and non-sctrict convex functions, every local minimum is a global minimum. Visually, a convex function “curves up”, without any bends the other way. What is convexity? A function is convex if and only if a segment joining two points on its curve always stays above the curve. The function is strictly convex when the inequality is strict. Caracterization of convex functions Sum of convex functions are also convex. A differentiable function of one variable is convex on an interval iff it lies above all of its tangents: A differentiable function of several variables is convex on a compact iff it lies above its linearization: A twice differentiable function of one variable is convex on an interval iff its second derivative is non-negative.