The best introduction to optimization methods book I've ever read is "Optimization by Vector Space Methods" by Luenberger. This is the book that opened my eyes

The best introduction to optimization methods book I've ever read is "Optimization by Vector Space Methods" by Luenberger. This is the book that opened my eyes to the generality of least-squares methods, the actual geometry of the problem, and how to apply it extremely generally. I read this before Boyd and Vanderberghe's "Convex Optimization", and I'm glad I did - it goes much more deeply into the intuition and exposition. It's not as well known as it should be, but it's a complete gem.