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Optimization for Industrial Problems

Suppose we have a function f (x) where the variable x may be a vector of many dimensions. We seek the point x∗ such that f (x∗) is the maximum value among all possible f (x). This point x∗ is called the global optimum of the function f (x). It is possible that x∗ is a unique point but it is also possible that there are several points that share the maximal value f (x∗). Optimization is a field of mathematics that concerns itself with finding the point x∗ given the function f (x).