Problem 1 Consider the problem minimize f(x) s.t. x € X where X = {2 € R² : x² + x² ≥ 1} and f(x) = 72. a. Find all point (s) satisfying a first order necessary optimality condition. Recall we studied two: FD-FONC and FONC. b. Which of the point (s) in part a satisfy a second order necessary optimality condi- tion? c. Which of the point (s) in part a are local minimizers?

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