I want to solve below minimization problem
\begin{equation*} \begin{aligned} & \underset{A, B}{\text{minimize}} & & ||Y-AB^T -D||_F^2 \\ & \text{subject to} && |A_i|_1 \leq a, \; i = 1, \ldots, k \\ &&& |B_j|_1 \leq a, \; j = 1, \ldots, k \\ &&& |(AB^T)_k|_1 \leq b, \; k = 1, \ldots, n \end{aligned} \end{equation*} where $Y \in \mathbb{R^{n \times n}}$, $A \in \mathbb{R^{n\times k}}$ ,$B \in \mathbb{R^{n \times k}}$, $D \in \mathbb{R^{n \times n}}$ is a diagonal matrix, $||_{1}$ denotes $l_1$ norm, $A_i$ is the $i^{th}$ column of $A$ matrix and $k < n$. I thought of solving this minimization problem using Proximal Alternating Learnized Minimization (PALM), but I am not sure about how to include $|(AB^T)_k|_1 \leq a$ constraint in the minimization algorithm. Is there any other way to solve this minimization i.e. without using PALM? I had posted the question on MathOverflow also, here is the link of it https://mathoverflow.net/questions/299843/l1-norm-constraint-on-product-of-2-matrix