Subgradient Methods
Subgradient methods are iterative optimization algorithms used to minimize non-differentiable convex functions. They extend gradient descent to handle functions that lack a unique gradient at some points by using subgradients, which are generalized gradients defined for convex functions. These methods are widely applied in machine learning, operations research, and engineering for problems like support vector machines and linear programming.
Developers should learn subgradient methods when working with optimization problems involving non-differentiable convex functions, such as in training support vector machines or solving large-scale linear programs. They are particularly useful in machine learning for handling L1 regularization (e.g., LASSO) and in distributed optimization scenarios where functions are not smooth. Their simplicity and applicability to a broad class of problems make them a foundational tool in convex optimization.