I had previously asked a question in which the problem was incorrectly specified. I am rephrasing it in this new question. The specific model is this one:
Let A $\in \mathbb{R}^{n \times m}$ and B and C $\in \mathbb{R}^{m \times n}$, all of them known. Let${\Vert\cdot\Vert}_F$ be the Frobenius norm of a matrix. Let X $\in \mathbb{R}^{n \times m}$ a matrix of unknowns and m>n.
\begin{align*} \text{min} \quad & \lVert X-A\rVert^2_F \\ \text{sujeto a} \quad & X*C = I \\ & \forall i,j \in \{1,2,...,n\}, (B*X)_{ij} \geq 0 \\ & \forall j \in \{1,2,...,n\}, \sum_{i=1}^{m} X_{ij} = 1 \end{align*}
It would also be interesting to be able to approximate the solution in a case of nxn matrices.
How can I solve this?.
Thank you in advance