First, Thank you very much to all the contributors to this website. My question is: What resources are available to study math programming, especially for students new to this area and selflearners. Personally, I think those that can balance well between theory, methodology and realworld applications are needed to be recommended. Thanks. 
I think this question was pretty much covered in this post. I just summarize it here: Nemhauser and Wolsey have an excellent book on mathematical programming you can start with that and if you are interested in the theory of mathematical programming you can go on to read Bertsimas and Tsitsiklis's book "Introduction to Mathematical Programming". Although it is named "Introduction to ..." Bertsimas's book is not an introductory book in any means. If you really like to torture yourself with the theory of polytopes I highly suggest Alexander Schrijver's book "Theory of Linear and Integer Programming". it is an amazing book but there is no examples :) For nonlinear programming nothing beats Bazaraa's book "Nonlinear Programming: Theory and Algorithms" in terms of theory. Also "Linear and Nonlinear Programming" by Ye and Luenberger is a great reference for applications. One easy way to get exposed to modeling questions is to get the AMPL book and download their educational software (free) and work through the examples. You will see a lot of different situations and how to model different systems. answered 19 Nov '09, 12:23 Mark ♦ 
I'd also suggest "Model Building in Mathematical Programming" by H. P. Williams, which gets a bit more into the practicalities of math programming models. Coming up with an efficient model to a specific problem is part science, part art, part trialanderror and part luck. It's also not addressed all that much in conventional texts. You might also look for math programming models in back issues of the journal Interfaces, and look at past Edelman award winners (on the INFORMS web site  might also be on scienceofbetter.org). You won't get the gory details of the models, but you'll get an idea of where math programming models are useful (and produce big returns). answered 19 Nov '09, 21:59 Paul Rubin ♦♦ Does INFORMS release any technical article on Edelman winners' work? I always wanted to see their work but never found any details. Williams book was a fantastic suggestion thanks.
(21 Nov '09, 04:43)
Mark ♦
I'm not aware of anything with what I would call "technical details" for the Edelman winners. Others might know better.
(27 Nov '09, 23:17)
Paul Rubin ♦♦

If you new to this area, perhaps you could start with 'Linear Programming'. At least, thats how i got hooked. If you have a strong math background, you could choose to start with nonlinear programming first (Bazaraa, Sherali, Shetty). For LP, my personal preference is the latest edition by Bazaraa, Jarvis, and Sherali, as well as the latest edition by Vanderbei. There are a few other good ones as well including Schrijver's book mentioned earlier. answered 20 Nov '09, 04:52 shiva 