How should I solve the following constrained optimization problem with Lagrange multiplier.
min L = $\frac{(Y-X^T\beta)^2}{2||x||_2^2}$ such that $||\beta||_2^2 \leq 1$
I know that I should change this to min $L = \frac{(Y-X^T\beta)^2}{2||x||_2^2} - \lambda (||\beta||_2^2-1)$ $\lambda >0$
$\frac{dL}{d\beta} = \frac{-2X(Y-X^T\beta)}{2||X||_2^2}-2\lambda\beta = 0$
$\frac{dL}{d\lambda} = -(||\beta||_2^2-1) = 0$
However, I am not sure how to proceed from now. Please help.