How to convert a nonlinear constraints into linear constraints

Question

I met problem, for example:

$\min x_1 + x_2 + x_3$
$\operatorname{sub} x_1^2 + 2x_1 + x_2^2 + 4x_2 + x_3^2 + 3x_3 \le 0 $

How to convert such nonlinear constraints into linear constraints?

Thank you so much

Answer 1

You cannot. The constraint models a spherical region, and thus impossible to represent using linear constraints (draw a circle on paper and then try to describe it using (a finite number) of straight lines...)