Ebook: Conjugate Duality and Optimization (CBMS-NSF Regional Conference Series in Applied Mathematics)

This monograph presents an excellent introduction to convex duality. If you want to understand duality via perturbations and its connection to lagrangian functions this is a great way to start. The book "Convex analysis" (by the same author) is probably more accurate and it has more material, but it was written in an ecyclopedic style, which is more useful as a reference.

One of the best things of this monograph, is that duality theory is introduced with several examples and applications: nonlinear programming, semi-infinite programming, Chebyshev approximation, stochastic programming, calculus of variations, etc. These examples are developed, in such a way that the reader can practice the theory that was previously introduced.

Also, the chapter of integral functionals is extremely useful for people interested in calculus of variations and optimal control.

Real and functional analysis is required (measure theory and basic Banach space theory), though. All in all, a great book.