What books do you recommend I should use as an introduction to convex analysis?

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A few years ago, I was in undergrad taking an introductory real analysis course. There was a problem I could not solve. I went to the TA. He was able to solve it using convexity. He recommended that I study convexity. What books do you recommend I should use as an introduction to convex analysis?

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A general reference for working with convexity (i.e. convex functions + sets) is chapters 1 and 2 of Boyd and Vandenberghe. It's available for free on Boyd's website.