Reference Request: Soft handed text on duality theory?

Question

Can anyone recommend a text on duality theory which includes basic formulation of the primal and dual formulation and some introduction to minimax problems? Preferably having some computation in finite dimensional vector spaces with plenty of examples.

Thanks ^_^

Answer 1

There are many (but of course closely related!) notions of "duality". By far the most powerful is the Fenchel-Rockafellar. This this 'technology', you can convert rather complicated problems into dual form in just one line of calculation. It some cases, the problem so-obtained is much easier to attack than the original. To get the ball rolling, start with this one-page material by Bauschke. For a more advanced exposition, see Nesterov or Bauschke.

Answer 2

Boyd and Vandenberghe is a good place to start. It makes the discussion of duality about as simple as possible, and it certainly has many good examples. The book is free online.