I'm interested in finding $\arg\min_{x \in X} (f(x) + \lVert x\rVert_2^2)$ where $X$ is a $[0,1]^n$, $f$ is Lipschitz but non-convex and we already have a procedure to find some $x^* \in \arg\min_{x\in X^*} \lVert x\rVert_2^2$, where $X^* = \arg\min_{x \in X}(f(x))$, that is we can find minimal values of $f$, and specifically one which minimizes the norm of the argument in the set that minimizes $f$.
$f(x)$ is some polynomial in $x_i$ which is linear with respect to each $x_i$ and with coefficients either $1$ or $-1$, for example $x_1 x_2 - x_1 x_3$
Using prox-linear algorithms I can find local minima of the sum, is there any way to use global minima of $f$ to improve this?
