Recently, I came across a modified L2 regularization term as stated in the equation below, where $\gamma$ is a positive number.
$$ \lambda'(w^Tw)^\gamma $$
I'm curious if a closed-form solution exists for this modified regularization term. Specifically, I'm interested in understanding whether analytical solutions exist for various gamma values or if numerical optimization methods are always necessary to find the optimal solution.
Has anyone encountered this scenario before? Are known results or strategies for dealing with L2 regularization raised to a power in a closed-form manner? Any insights or references would be greatly appreciated.