Nonlinear Programming Example Problem

A nonlinear programming problem (NLP) is an optimization problem where the objective function or some of the constraints are nonlinear. Consider the following problem:

This is the well-known Rosenbrock function that is particularly hard for nonlinear solvers because of its shape. The animation below describes the features of this problem, as well as the various ways solvers may try to provide a solution. The next 3 animations show how different the solution trajectories can be for different solution algorithms implemented in different solvers: