Nonsmooth Analysis

Nonsmooth analysis is a branch of mathematics that studies functions which lack smoothness, meaning they might have sharp corners, jumps, or edges. Unlike smooth functions that can be easily differentiated everywhere, nonsmooth functions require specialized tools to analyze their behavior, especially in optimization problems. It helps us understand how to find the best solutions even when the function isn’t nicely shaped. This area is important in various fields like economics, engineering, and machine learning, where real-world problems often involve nonsmooth situations.