  Let $n\geq 2$ and $\mathbb K $ be a number field of characteristic $0$.
Jacobian Conjecture asserts for a polynomial map $\mathcal P$ from $\mathbb K
^n$ to itself, if the determinant of its Jacobian matrix is a nonzero constant
in $\mathbb K $ then the inverse $\mathcal P^{-1}$ exists and is also a
polynomial map. This conjecture was firstly proposed by Keller in 1939 for
$\mathbb K ^n=\mathbb C^2$ and put in Smale's 1998 list of Mathematical
Problems for the Next Century. This study is going to present a proof for the
conjecture. Our proof is based on Dru{\.{z}}kowski Map and Hadamard's
Diffeomorphism Theorem, and additionally uses some optimization idea.
