So I have a $n$-dimensional polynomial that takes in a vector $\vec x$
$$ f(\vec x) = x_1x_2 + 2x_2 + ... $$
such that $f(\vec x)$ is some arbitrary linear combination between various $x_i$'s and products of $x_i$'s
I want to minimize $f(\vec x)$ subject to
$$ a_1 \leq x_1 \leq b_1 $$ $$ a_2 \leq x_2 \leq b_2 $$ $$ ... $$ $$ a_n \leq x_n \leq b_n $$
I know that $LP$ linear programming problems are guaranteed solvable in polynomial time, so I wanted to know if my polynomial is considered a linear programming problem, such that it could be solved in a polynomial amount of time. Thank you