Generally quadratic convex problem with one non-convex term

How would you approach a standard convex quadratic problem with convex constraints but one non-convex term ? Say $|x|^{0.4}$.

$$min_x frac{1}{2} x^{T}Qx + g^Tx + c^T mathrm{sign}(x) |x|^{0.4} $$
subject to $$Axleq b$$

Where $|cdot|, mathrm{sign}()$ are element-wise.

Is there any other way to solve the problem within convex framework ? What`s the best way to approximate if the dimensions are large ?

This is similar to Reformulate a strictly convex QP problem containing absolute value term but here there is a power term.