Proximal gradient method

The proximal gradient method is an algorithm used to optimize complex functions often found in machine learning and statistics. It works by breaking down a difficult problem into simpler steps: first, it takes a small move in the direction that reduces the main part of the function, then it adjusts this move considering additional constraints or penalties. This process iterates, gradually approaching an optimal solution. It is especially useful for problems involving both smooth components (which change gradually) and non-smooth parts (which introduce constraints or promote sparsity).