I wonder if I can solve the following with ADMM:
$$ \min_{A,C}||C||_* +\lambda||X-A||_F^2 $$ with the constraint $$A=AC$$.
My doubts are because usually the general form for ADMM is $$ \min_{x,z} f(x) + g(z) $$ with the constraint $$Ax+Bz=c$$
and in my problem, I have multiplication of A and C. What should I do ?