lecture 10, slide 7

Hi,

In slide 7 of lecture 10, I don't understand how we can get from max to min in the last two lines.

optml_duality.jpg

Thank you in advance for your help.

Top comment

I think there are errors on the slide, and it should look like this:

Screenshot 2021-07-01 at 09.41.04.jpg

Does that answer your question?

Hi, it looks to me like something is going wrong on this slide. I think the definition of f*(x) on this slide is inconsistent with the course's definition of the Fenchel conjugate (I get something else). I'll double-check and get back to you. Thanks!

Top comment

I think there are errors on the slide, and it should look like this:

Screenshot 2021-07-01 at 09.41.04.jpg

Does that answer your question?

Many thanks for your reply.

Yes, that answers my question. However, I have two more questions:

The penultimate line should be

$$ argmax \{-\frac{1}{2}||b||^2 - \frac{1}{2}||b-u||^2 \} $$

right?

Also, would it be possible to have a more detailed derivation of the conjugate of \(f(w)=\frac{1}{2}||w-b||^2\) ?

Hi Sepideh,

Ah, no the penultimate line is correct, but the conjugate should have been

Screenshot 2021-07-01 at 10.41.38.jpg

My derivation looked like this (where I set the derivative to zero to find \(w\))

Screenshot2021_06_30_175538.jpg

All clear now, thank you!

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