# Find local and global minimizers

Consider the problem:

minimize $f(x)=x_1$

subject to $x_1^2+x_2^2≤4$, $x_1^2≥1$.

Find all local minimizers for the problem, and determine which of those are also global minimizers.

My answer: By graphing the feasible set, and according to definitions of local and global minimizer, is the local minimizers $x_1=1$ and $-2$? And $-2$ is the global minimizer. Are they correct?

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