Abstract
This introductory chapter reviews a few selected major methods for optimization and mathematical modeling available today. The topic is extremely broad, so the focus is on methods that not only have sound theoretical ground, but more importantly, exhibit good performance in practice. Results from optimization theory and convex analysis–such as theorems of the alternative–are only mentioned and used to prove the necessary and sufficient conditions for mathematical programming. On the other hand, algorithms are described in enough detail so that the reader can understand under what circumstances and why they should be expected to work well in practice and also implement them from scratch if the need arises.
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