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I've been getting myself involved with this topic and would like to read more to gain a conceptual understanding of the various techniques and what each one is trying to achieve and their 'idea' behind achieving it. Basically the 'big-picture' view of things excluding the complicated math if possible.

I've read numerous articles on the web and TCS too :) but still would like to know some good references for the layman (i.e. if you were to explain the various concepts/ideas to your wife/mother/child what you recommend them?) I know they wouldn't all be listed in one book but even if they are spread out across books that's fine.

I'm quite interested in learning about nonlinear programming, semi-definite programming, convex optimization, I'm fairly well versed with linear/integer programming and do have a decent background in algorithms and a strong CS background too :)

I may not have a strong mathematical background as probably required by these topics and before I develop it I'd like to have some 'fun' understanding the 'what, why and how' at a more humane level before diving into the math :)

What would be some good references for the above? Good books/links covering other aspects of optimization but not listed above would be welcome to.

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I don't understand the background you list. How can you be "fairly well versed with linear/integer programming" and "a strong CS background", while still saying "I may not have a strong mathematical background as probably required by these topics". – Artem Kaznatcheev Oct 28 '12 at 0:18
It's saying that although I'm capable of parsing math heavy texts I don't prefer too. In some cases I may have to spend a lot of time to understand the math in case of semidefinite programming. Hence just stating my 'qualification' but also setting the expectation of the references. I've majored in CS but not heavily focused in optimization to be able to make perfect sense of all the math just be reading a book. – PhD Oct 28 '12 at 19:33

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This is a very vast topic. For nonlinear optimization the book by Bertsekas is a standard reference. For convex optimization you should look at Boyd and Vandenberghe. For linear programming, the book by Schrijver is a reasonable (but dense) source.

But you should also look at course material. Each of the authors mentioned above also has course material/lecture slides that might be useful.

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