Question from Boyd's Optimization Book

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The discussion centers on a mathematical expression from Stephen Boyd's "Convex Optimization," specifically regarding the supremum of a quadratic form constrained by a norm. The user is seeking clarification on the equality involving the supremum of u^TP_i^Tx under the constraint ||u||_2 ≤ 1, suggesting it relates to the Cauchy-Schwarz inequality. Other participants confirm that the expression indeed follows from the Cauchy-Schwarz inequality, emphasizing its role in deriving the result. The conversation highlights the importance of understanding these foundational concepts in optimization. Overall, the discussion aids in clarifying a specific mathematical concept from Boyd's work.
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Hi,

I am reading Convex Optimization from Stephen Boyd's book on my own and I am stuck at math he mentions on Pg. 157 of his book which can be found here.

How does he write the following:

sup{uTP^{T}_{i}x | ||u||2 ≤ 1} = ||P^{T}_{i}x||2

Thanks guys
 
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