Abstract
This chapter presents the theory of general nonlinear minimax approximations. The most powerful argument in favor of general theorems is that they apply automatically to many important special cases. The theorems presented in the chapter exemplify this point. There are no algorithms for obtaining general nonlinear minimax approximations, but it should be possible to derive methods that are effective for many approximation problems. The chapter also presents the characterization of nonlinear minimax approximations where the algorithms for obtaining minimax approximations depend on the fact that the final error curve must have extrema with calculable signs.
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