01 - Good objective functions - Functions with Lipschitz continuous gradient (L-smooth)

The goal of video is to understand the functions that have Lipschitz continuous gradient. This class of functions sometimes called L-smooth functions. What does the problem say? What property does a function satisfy if it has a Lipschitz continuous gradient. We will see that it can be bounded by a quadratic function. What is our approach? We start with fundamental theorem of calculus. Then we will be using directional derivative to convert the traditional derivative to inner product. Finally, using Cauchy-Schwarz inequality we proof the desired inequality.