15
$\begingroup$

I have taken some courses in Convex optimization. Now I would like to know a little bit more about the pure mathematical side. Is there any good books in convex analysis? I have read and worked with Boyds Convex Optimization book. Is there any video lectures anywhere? It would be nice as well. Thanks

$\endgroup$
5
  • 1
    $\begingroup$ For pure convex analysis there is the famous R.T Rockafellar press.princeton.edu/titles/1815.html $\endgroup$ – math Jan 12 '13 at 16:24
  • 1
    $\begingroup$ Does anyone know any online course on convex analysis? $\endgroup$ – user25004 Jan 27 '14 at 5:29
  • $\begingroup$ @user25004 im pretty sure stanford has an online course (at least video lectures) on the subject matter. $\endgroup$ – Winston Oct 8 '14 at 17:23
  • $\begingroup$ @ZMI Are you talking about convex optimization or convex analysis? I am asking about convex analysis. $\endgroup$ – user25004 Oct 10 '14 at 21:39
  • $\begingroup$ Yeah it might actually be convex optimization now that I think of it. I think he does the basics in convex analysis but if you've already studied Boyds book that might be too basic. $\endgroup$ – Winston Oct 11 '14 at 10:15
5
$\begingroup$

I'm a big fan of the first 50 pages of Ekeland and Temam. It's a short, clear, beautiful explanation of the basics of convex analysis. I also like Rockafellar's books Convex Analysis, and also Conjugate Duality and Optimization.

Other books I recommend looking at: Introductory Lectures on Convex Optimization: A Basic Course by Nesterov, Convex Analysis and Nonlinear Optimization by Borwein and Lewis, Convex Analysis and Optimization by Bertsekas and Nedic, Convex Optimization Theory by Bertsekas, Nonlinear Programming by Bertsekas.

I've heard good things about the book Nonsmooth Analysis and Control Theory by Clarke.

$\endgroup$
2
  • 1
    $\begingroup$ You mean Conjugate Duality and Optimization, right? The book Conjugate Duality in Convex Optimization was written by Radu Bot and published by Springer in 2010. $\endgroup$ – xFioraMstr18 Oct 31 '20 at 17:50
  • $\begingroup$ @xFioraMstr18 yes, thank you for catching that error. I just edited this answer accordingly. $\endgroup$ – littleO Oct 31 '20 at 17:58
4
$\begingroup$

There is a book by Jean-Baptiste Hiriart-Urruty and Claude Lemaréchal called "Fundamentals of Convex Analysis" that I thought was great. It might not be exactly what you're looking for, as it goes through a lot of basics as well. But it's a very clear book, very easy to read despite being rigorous.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.