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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

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For pure convex analysis there is the famous R.T Rockafellar – user8 Jan 12 '13 at 16:24
Does anyone know any online course on convex analysis? – user25004 Jan 27 '14 at 5:29
@user25004 im pretty sure stanford has an online course (at least video lectures) on the subject matter. – ZMI Oct 8 '14 at 17:23
@ZMI Are you talking about convex optimization or convex analysis? I am asking about convex analysis. – user25004 Oct 10 '14 at 21:39
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. – ZMI Oct 11 '14 at 10:15

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.

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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 in Convex 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.

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