Nocedal and Wright is good. +1 also to the suggestions for Boyd and Vandenberghe. I really like Boyd's writing in general; he has coauthored some good review ar

Nocedal and Wright is good. +1 also to the suggestions for Boyd and Vandenberghe. I really like Boyd's writing in general; he has coauthored some good review articles on proximal algorithms and ADMM. A couple of other suggestions: Nesterov's Introductory Lectures on Convex Optimization. This one is pretty tough sledding, but I found the perspectives in the first chapter particularly to be enlightening. It seems like there's a newer Springer book which is probably an expansion on this. Bertsekas's Nonlinear Programming. Bertsekas has written a lot of books, and there's a fair amount of overlapping going on. 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.