Optimisation non convexe

Aidez-moi SVP à décomposer les fonctions suivantes en soustraction de deux fonctions convexes :
\begin{align*}
f_{1}(x,y)&= 1+(x^{2}+2)y+xy^{2},& x\in [1,2],\ y\in [-10,10] \\
f_{2}(x,y)&= 2x^{2}-1.05x^{4}+y^{2}-xy+\frac{1}{6}y^{6},&x\in [-2,4],\ y\in [-2,4]\\
f_{3}(x,y)&= -2x^{2}-1.05x^{4}+y^{2}-xy+\frac{1}{6}y^{6},&x\in[-2,4],\ y\in[-2,4]\\
f_{4}(x,y)&= (x-2y-7)^{2}+(2x+y-5)^{2}, &x\in [-2.5,3.5],\ y\in[-1.5,4.5]\\
f_{5}(x,y)&=(1+((x+y+1)^{2})(19-14x+3x^{2}-14y+6xy+3y^{2})) \\
&\qquad (30+((2x-3y)^{2})(18-32x+12x^{2}+48y-36xy+27y^{2})),& x\in[-2,2],\ y\in [-2,2]\\
f_{6}(x,y)&= (x-1)(x+2)(y+1)(y-2)y^{2}, &x\in [-2,2],\ y\in [-2,2]\\
f_{7}(x,y)&= -(x-1)(x+2)(y+1)(y-2)y^{2}, &x\in [-2,2],\ y\in [-2,2]\\
f_{8}(x,y)&=4x^{2}-2.1x^{4}+\frac{1}{3}x^{6}+xy-4y^{2}+4y^{4},&x\in [-1000,1000],\ y\in [-1000,1000]\\
f_{9}(x)&=12x^{2}-6.3x^{4}+x^{6}+6y(y-x),& x\in[-1000,1000],\ y\in[-1000,1000]\\
f_{10}(x)&=-\frac{1}{(\sqrt{x^{2}+y^{2}}-0.3)^{2}+0.01}-\frac{1}{(\sqrt{x^{2}+y^{2}}-0.9)^{2}+0.04}+6,&x\in [-1,2],\ y\in [0.001,3]
\end{align*} Merci d'avance.