I have this function $f (x,y) = x$ with constraints $h_1 (x,y) = -(x+1)^2 -y^2+1 \leq 0$ and $h_2 (x,y)=x^2+y^2 -2 \leq 0$.
With the Lagrange multiplier rule:
$$\lambda_0 \nabla f (x,y) + \mu_1 \nabla h_1 (x,y) + \mu_2 \nabla h_2 (x,y) = 0$$
I get:
$$\lambda_0 + \mu_1 (-2x-2 +2y)+ mu_2 (2x+2y)=0$$
But how should I solve this ?
Thank you !