Consider the optimization problem min f (x) s t x S where S Rn Prove that x is optimal for the given optimization problem if and only if x is optimal for min f (x) s t x S 3 for any , R where 0 Remember proving A if and only if B requires you to prove two statements If A then B and If B then A

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Consider the optimization problem min f (x) s t  x S where S Rn  Prove that x is optimal for the given optimization problem if and only if x is optimal for min f (x) s t  x S 3 for any , R where   0  Remember proving  A if and only if B  requires you to prove two statements   If A then B  and  If B then A

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Question: Consider the optimization problem min f (x) s.t. x S where S Rn. Prove that x is optimal for the given optimization problem if and

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