Convex Analysis
by Ralph Tyrrell Rockafellar · first published 1970
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…This one seemed to be the one that has the most nuts and bolts about the basics of optimization. EDIT: If you want more understanding of convexity beyond what's presented in these books, Rockafellar's Convex Analysis is helpful.
on “Ask HN: Literature for mathematical optimization?” ↗The usual good starting point is Boyd’s Convex Optimization, for a relatively rigorous but also quite practical book. The second usual, quite a bit more rigorous case is Rockafellar’s Convex Analysis, but this one deals only with general analysis as opposed to also including applications and algorithms. I highly recommend Boyd’s book, even for a mathematician ;) since it gives a lot of great motivation…
on “A Classical Math Problem Gets Pulled into the Modern World” ↗Convex analysis by Rockafellar is pretty hard for a beginner. It's a research monograph. I would recommend "Fundamentals of convex analysis" by Hiriart-Urruty & Lemaréchal
on “Ask HN: Literature for mathematical optimization?” ↗…convex, then it is continuous (proof is not very difficult but is in Fleming, Functions of Several Variables). IIRC convex implies differentiable almost everywhere (maybe proof in R. T. Rockafellar, Convex Analysis). The epigraph is the graph of f and everything above it, and it is a convex set so has supporting hyperplanes and is the intersection of all the closed half spaces from its supporting (tangent) hyperplanes…
on “An Intro to Integer Programming for Engineers: Simplified Bus Scheduling” ↗