What is strongly convex?

A function is said to be strongly convex if its second derivative is positive and bounded away from zero over its entire domain. In other words, a function is strongly convex if it has a strictly increasing curvature throughout its domain. This property makes it easier to optimize functions as there is a unique minimum, which is also global. Strongly convex functions possess many important properties such as Lipschitz continuity, uniqueness of the minimizer, and more efficient convergence rates for iterative optimization algorithms. Applications of strongly convex functions can be found in areas of machine learning, optimization, and computer vision.