# How to proceed with such a constraint?

Hello again.
I have been trying to formulate the following constraint to work with CVX:$$C == \begin{bmatrix} A^TA & A^TB \B^TA & B^TB \end{bmatrix} = \begin{bmatrix} A^T \ B^T \end{bmatrix}\begin{bmatrix} A & B\end{bmatrix} = MM^T$$
Where both, A and B are variables.

I understand this isn’t linear. If I am not mistaken this is a bilinear form, right? So how does one proceed with such a constraint? By “proceed,” I mean any path that will allow me to either formulate this in a way CVX will enjoy or even an estimation that may work. I am also not looking to be spoon fed but to be guided where to go from here. Is attempting such a formulation even possible with CVX?

EDIT: Even just providing a name or subject for such a constraint for me to research would be of great benefit, as I am not even sure what type of constraint this is.

You have a quadratic. I presume your constraint (the point of the right-hand side) is that C is psd? If so, depending on the rest of your problem specification, you may be able to solve it with PENLAB under YALMIP. Whether PENLAB will succeed in finding even a local optimum is another matter.

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Perplexabot: it is time for you to read the FAQ again. This constraint is completely off limits for CVX, and if you actually follow the FAQ properly you would not have asked the question.

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Thank you for the tips and your time. I will experiment with what you are saying.