I have the following function in $X \in R^{n \times k}$
$$f(X) = -4A X\Lambda_1 + 4(X\Lambda_1 X^T X\Lambda_1) - 4A^TXY\Lambda_2Y^T + 4XY\Lambda_2Y^TX^TXY\Lambda_2Y^T$$
where $A \in R^{n \times n}$, $Y \in R^{k \times k1}$, $\Lambda_1 \in R^{k \times k}$ and $\Lambda_2 \in R^{k1 \times k1}$, and $\Lambda_1 , \Lambda_2$ are diagonal matrices. How can I find Lipschitz constant of the above function with respect to frobenious norm? Would it be possible to find local Lipschitz constant I know ||X||? The f function is gradient with respect to X and I am trying to do a gradient descent, so, I will have bounds on ||X||.