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# Find the minimum value of ||x||1 subject to ||x||2 = 1 in R2. Which x achieves such minimum?

Find the min value of the 1 norm x subject to 2 norm x

Find the minimum value of ||x||1 subject to ||x||2 = 1 in R2. Which x achieves such minimum?

For any ﻿ ( x , y ) ∈ R ​ 2 ​ ​ ﻿ , we have ﻿ ∣ ∣ ( x , y ) ∣ ∣ ​ 2 ​ ​ = √ ​ x ​ 2 ​ ​... View the full answer

• hi.. im wondering if \$||x||_{infty} = max (|x|, |y|) since according to theorem that ||x||_{1} = |x|+|y| so can we => ||x||_{1} = max (|x|, |y|) ? thank you
• danie0723
• May 02, 2018 at 2:27am
• is it ||x||_1=|x|+|y| in your definition? Then i would have to redo it. In that case answer would be minimum value 0 , which is attained at 3pi/4 and -pi/4
• Mathwarrior
• May 02, 2018 at 5:31am

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