I am trying to minimize the function $f(X) = \|A - XYY^TX^T\|_F^2$ where the gradient of $f$ follows the bound given belew where $A,X,Y \in R^{n \times n}$

$$\|\nabla f(X_1) - \nabla f(X_2)\|\leq L\|X_1-X_2\|^n_F,\ \forall X_1,X_2, $$

To solve the above problem I am trying to perform gradient descent but the Hessian of the function is 0, hence I a am not able to decide the step size. I posted a question about hessian here Bound on hessian when Lipschitz gradient is bounded. I not able to get bound on the step size so that gradient descent does not diverge.


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