$.$ Consider the following optimization problem

min $($x$12)2($x$23)2$

s$.$t$.$ g$1$ : $3$x$12$x$2+6<=0$

g$2$ : $$x$1+$ x$23<=0$

g$3$ : $$x$12<=0$

$($a$)$ Derive the Lagrangian dual problem

$($b$)$ Write KKT conditions

$($c$)$ Identify the points satisfying KKT conditions

$($d$)$ Identify maximum$/$minimum points