I have two matrices $A$ and $B$ of size $n \times n$. I am trying to find the proximal operator of the below functions i.e. assume one of the matrices constant while finding the $L1$ proximal operator of the other matrix $$ g(B) = |AB|_1 \quad f(A) = |AB|_1$$ where $L1$ norm of a matrix is the absolute sum of all the elements. I am not able to find a way to solve the above problem. I would be really grateful if someone could give a pointer to it. There is a similar question Finding analytically proximal operator of $g(P)=\|PX\|_1$ using Moreau decomposition , but I was not able to find the analytical solution to it.
2026-02-23 08:24:23.1771835063
Proximal Operator / Mapping of Multiplication of Two Matrices
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