What is Moreau’s Decomposition Theorem?

Let be a convex function. Moreau’s Decomposition Theorem is the following result: Theorem (Moreau Decomposition). For all , , where is the proximal operator for and is the convex conjugate of . Here is the proof: Let . Then, The second equivalence is a result involving convex conjugates and subdifferentials (see this post for statement […]

What is Moreau’s Decomposition Theorem?