Find local and global minimizer(s)? Consider the problem:
minimize $f(x)=x_1$ subject to
$(x_1-1)^2+x_2^2=1$, $(x_1+1)^2+x_2^2=1.$
Are there any local minimizers? Are there any global minimizers?
Is $(-2,0)$ both the local and global minimizer?

You constrain your function to the intersection of the circles of radius 1 centred at $(-1,0)$ and $(1,0)$, i.e. you minimize the function f over the set $\{(0,0)\}$. Consequently, $(0,0)$ is the only local and global optimiser.
