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i am looking for a short proof for a theorem of a book:

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$f\in S^2_\mu(\mathbb{R}^n)$ means that f is strongly convex with parameter $\mu$ i.e

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2.1.17 you can find in enter image description here

theorem 2.1.11 says i just have to apply 2.1.17 but i don't know how to do it

thanks for your help

Suzu Hirose
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Felix Wilde
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    What book is this from? – littleO Oct 07 '22 at 12:28
  • The definition 2.1.2 describes $S^1$, but the upper text discusses $S^2$, so maybe you haven't looked in the correct place for the right definition. – Suzu Hirose Oct 07 '22 at 12:55
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    introductory lectures on convex optimization: a basic course by Yurii Nesterov – Felix Wilde Oct 07 '22 at 12:57
  • $S^2$ means that the function ist two times differentiable – Felix Wilde Oct 07 '22 at 12:58
  • The reason this proof is abbreviated like this is because it's almost a duplicate of a previous proof in the book, with the small change from convex to strongly convex. I'm a little bit mystified why you asked the question, unless you skipped over most of the book and just landed at this proof. Surely it would be a good idea to read the entire chapter otherwise of course you will be mystified when you just jump onto a particular theorem on a particular page. – Suzu Hirose Oct 09 '22 at 03:44

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