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# Chapter 9. Optimization

Often, in scientific computing, we are required to find the value of x for which a function f(x) will attain a maximum or minimum value. In other words, we want to maximize or minimize f(x). This process is termed as numerical optimization and can be summarized as follows: In the preceding formula, x represents a vector of variables also known as the unknowns or parameters, f is the function of x we want to maximize or minimize known as the objective function, zi is the constraint functions that x must fulfill, and N and M are sets of indices. Optimization problems are used in mathematics, finance, and computer science to ...

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