Tychonov regularization (regularized least-squares), i.e., choosing $x$ to minimize $\|Ax-y\|^2 + \mu \|x\|^2$, with $\mu >0$
Suppose that $x$ minimizes $J_1(x) + \mu J_2(x)$, for some value of $\mu>0$, but you'd like to find a point with a smaller value of $J_2$, if possible. You should