The quadratic sandwich

If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your function that tells you exactly how well-behaved it is. If the sandwich is tight, life is good. If one slice of bread is missing, things get ugly fast.