Question from Boyd's Optimization Book

newphysist

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{u^TP[itex]^{T}_{i}[/itex]x | ||u||₂ ≤ 1} = ||P[itex]^{T}_{i}[/itex]x||₂

Thanks guys

jasonRF

I didn't attempt to find this in the book, but to me this looks like a direct result of the Cauchy-Schwarz inequality.

http://en.wikipedia.org/wiki/Cauchy%...arz_inequality

jason

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newphysist	Question from Boyd's Optimization Book Tweet 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{u^TP[itex]^{T}_{i}[/itex]x \| \|\|u\|\|₂ ≤ 1} = \|\|P[itex]^{T}_{i}[/itex]x\|\|₂ Thanks guys

jasonRF	I didn't attempt to find this in the book, but to me this looks like a direct result of the Cauchy-Schwarz inequality. http://en.wikipedia.org/wiki/Cauchy%...arz_inequality jason