nonlinear programming

Nonlinear programming is a type of optimization problem where the objective function or constraints are not linear. This means they cannot be expressed as simple straight lines or planes, but involve curves or more complex relationships. These problems arise when real-world systems have essential nonlinear features that linear models cannot capture.1

For instance, the optimal shape of a protein molecule or the risk associated with an investment portfolio are examples of nonlinear relationships. The field has roots in problems like finding the curve that minimizes travel time, explored by mathematicians like Newton and Leibniz. Modern nonlinear programming utilizes algorithms that iteratively refine guesses to find optimal or near-optimal solutions, and these techniques are widely applied in fields like finance, economics, and engineering.12