Nonsmooth optimization

Nonsmooth optimization involves finding the best solution to a problem where the function you're optimizing isn't smooth or differentiable everywhere—meaning it may have sharp corners or abrupt changes. Traditional optimization methods rely on derivatives (slopes), but nonsmooth problems require special techniques that can handle these irregularities. This field is important in many real-world applications like machine learning, finance, and engineering, where systems often have abrupt shifts or structures that make standard methods inadequate. Essentially, nonsmooth optimization seeks optimal solutions even when the landscape of possibilities isn’t smooth or straightforward.