On a more concrete level, nonlinear optimization seeks to minimize or maximize a real-valued function, subject to a system of constraints defined by functional inequalities and equations. What makes the problem a nonlinear program is that at least one of the functions is nonlinear. This course begins with classical results that were obtained before calculus, then describes the seminal contributions of Newton, Gauss, Lagrange, and Cauchy. Modern algorithms begin in the 1950's with the advent of the computer, and the theory extends to convex analysis and duality. Applications include natural phenomena, engineering design, and economic equilibria.
Special attention is given to certain classes of nonlinear forms, such as quadratic forms.