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Optimization means choosing the best among a set of options. It arises in engineering when trying to choose the best among different system designs or courses of action, and in the physical sciences when trying to predict how nature will behave. It also arises in statistics, when trying to describe reality in a way that best fits available data. Optimization becomes challenging, and mathematically interesting, when the number of options is too large to allow evaluating each one individually. In such situations, optimization methods can use a problem's structure to quickly find the best option without evaluating each one. Challenges in optimization also arise when options cannot be evaluated perfectly, when evaluating an option takes a long time.

Researchers within CAM consider many different kinds of optimization problems, each with its own special structure and applications, including convex optimization, combinatorial optimization, continuous optimization, optimization via simulation, and global optimization of expensive functions.