subdifferential

The subdifferential is a mathematical concept used to analyze functions that may not be smooth or differentiable everywhere. For a function that might have sharp corners or flat areas, the subdifferential at a point is the set of slopes (called subgradients) that support the function from below, meaning they touch the function at that point without crossing it. This helps us understand how to optimize or work with such functions, especially in areas like machine learning and optimization, by providing a generalized way to measure how the function behaves locally, even where ordinary derivatives don’t exist.