# Proximal operator of matrix norm

How to calculate proximal operator of $$F(X,Y) = f(X,Y) + \lambda(||X||^2 + ||Y||^2)$$ where $X$ and $Y$ are matrices. The problem is to minimize the given function with respect to X and Y.Idea is i want to use proximal gradient descent.For that i need to calculate proximal operator of given function.

• Have a look here - math.stackexchange.com/a/2444238/33. All needed is someone to take care of your case which is the sum of two matrices. – Royi Sep 25 '17 at 8:20
• The sum of two matrices is real problem. – Arun Sharma Sep 25 '17 at 10:00
• I do not understand exactly which part of $F$ you consider as the 'differentiable' part, and which one you consider as the 'proxable' part. Please elaborate. – Alex Shtof Sep 26 '17 at 8:47
• f(X,Y) is considered as differentiable part where as the remaining part is proxable. My problem is how to handle multiple variable norms for a proximal gradient descent. – Arun Sharma Sep 27 '17 at 5:55
• Could you specify which matrix norm are you referring to? Is it Frobenius? – Royi Aug 3 at 8:54