ABSTRACT
This chapter presents several numeric techniques for approximating the optimal solution to nonlinear programs. It begins with a classic Calculus I application of a nonlinear program. The chapter present an algorithm called Newton’s method for numerically approximating the solution to nonlinear programs. Newton’s method relies on the derivative of a function. But not every function is differentiable. The chapter presents a search method, called the golden section method, that does not rely on the derivative. It discusses a technique for solving constrained nonlinear optimization programs called the method of Lagrange multipliers which utilizes gradients. The discussion is limited to programs involving two decision variables and one constraint, though these ideas can be extended to any number of variables and constraints. The chapter also describes a specific type of integer program called a binary integer program where the decision variables are required to be either 0 or 1.
