# Reformulation of a Frobenius norm maximization problem

This question is extended from this question

The original problem is to maximize the Frobenius norm of a matrix product

$max_{X\in \mathbb{D}}||B^TXA ||_F$, where $\mathbb{D}$ is the doubly stochastic matrix set

One challenge is that the size of matrix $X$ is big and I would like to reformulate it into a low memory requirement formulation.

I have tried to consider the $l_1$ version of the problem.

But yet the performance is not too good. (Mentioned in here)

Any good suggestion?

• Rein, I answered the $\ell_1$ vs. Frobenius part of this question for you over on Math.SE: math.stackexchange.com/questions/374279/… That answer has not changed. When I recommended posting a question over here, it was specifically to ask about the computational challenge of implementing a large-scale version of your problem. As written, I'd say this question is enough of a duplicate of the Math.SE question to recommend closure---but a good edit should take care of that. – Michael Grant Apr 27 '13 at 14:05
• @MichaelC.Grant Thanks, I have modified the question. – Rein Apr 27 '13 at 14:28
• Do you want to minimize or maximize the Frobenius norm of $B^{T}XA$? Michael Grant's answer below is written in terms of a minimization. – Brian Borchers Apr 27 '13 at 17:35
• Wow, I just noticed that. If you do indeed want maximization then all bets are off, this is a non convex problem, and nearly all of what I have said in both posts is wrong. – Michael Grant Apr 27 '13 at 18:51
• I have deleted my answer for now. I can always restore it with edits if we decide that's appropriate. – Michael Grant Apr 27 '13 at 20:07