Global minimum of sum of a non-convex and convex function, where minima of the non-convex function can be found

I’m interested in finding $argmin_{x in X} (f(x) + lVert xrVert_2^2)$ where $X$ is a $[0,1]^n$, $f$ is Lipschitz but non-convex and we already have a procedure to find some $x^* in argmin_{xin X^*} lVert xrVert_2^2$, where $X^* = argmin_{x in X}(f(x))$, 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?