What would be some good books to read on duality theory - both in combinatorial and convex optimization?


asked 29 May '12, 18:16

Sid's gravatar image

accept rate: 18%

For convex optimization, you could do worse than starting with Luenberger's Linear and Nonlinear Programming. I don't know whether that would be sufficient coverage for your needs, but the book is written well and accessible with a reasonable mathematical background.


answered 30 May '12, 18:29

Paul%20Rubin's gravatar image

Paul Rubin ♦♦
accept rate: 19%

Thanks for the response. I'm very familiar with the basic duality covered in books like Papadimitriou's Comb Opt. and Bertsekas' Nonlinear Programming so if you know about some more advanced books, that would be great!

(30 May '12, 22:19) Sid

Start with Bertsimas's "intro to linear programming" and then read Bazaraa and Shetty's nonlinear optimization book. What you need is a deep understanding of three concepts 1) Separating hyperplanes 2) Farkas Lemma 3) Duality

Think about how separating hyperplanes can describe duality. If you get that everything else is easy.

If those books are easy for you then you can go on to read Schrijver's book "Theory of Linear and Integer Programming" but it is very hard for the beginners.


answered 30 May '12, 22:29

Igor%20Pangal's gravatar image

Igor Pangal
accept rate: 0%

I just read a few sections of Bazaraa's book on NLP. It is easy to read and very insightful: I was able to understand what I was looking for at a glance.

(31 May '12, 12:58) Thiago Serra

I recommend Bazarra et al.'s linear programming book. It's the book that I always use for duality and LP.

(31 May '12, 15:26) lamclay

It is a little bit classical but one of the best references on duality theory is a paper by Geoffrion: "Duality in Nonlinear Programming: A Simplified Applications-Oriented Development," SIAM Review, Vol. 13, No. 1, Jan., 1971. It may be a little bit hard to understand but it is worth to spend the time.

A more recent reference is from "Nonlinear Optimization" book by Ruszczynski. Chapter 4. Good luck!


answered 05 Jun '12, 11:58

Burcu%20Keskin's gravatar image

Burcu Keskin
accept rate: 0%


@Burcu: Welcome to OR-X!

(05 Jun '12, 18:09) Paul Rubin ♦♦

I've just stumbled across the following: Convexity, Duality and Lagrange Multipliers, developed by Bertsekas. Judging from your reply to Paul Rubin's answer, it might be what you're looking for. From the Preface:

These topics include Lagrange multiplier theory, Lagrangian and conjugate duality, and nondifferentiable optimization. The notes contain substantial portions that are adapted from my textbook “Nonlinear Programming: 2nd Edition,” Athena Scientific, 1999. However, the notes are more advanced, more mathematical, and more research-oriented.

Hope it helps!


answered 01 Jul '12, 11:58

yeesian's gravatar image

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edited 01 Jul '12, 12:03

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Asked: 29 May '12, 18:16

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Last updated: 01 Jul '12, 12:03

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