Find global optima for problems with time-consuming objective function evaluations, including black box models. The surrogateopt function in Global Optimization Toolbox™ builds and optimizes a surrogate function in place of the expensive function. This derivative-free method can be applied to nonconvex problems. 

The problem solved in the video is to determine the optimal position and angle of a cannon to fire a projectile as far as possible over a wall. Evaluating this objective function requires solving an ODE. A nonlinear constraint is included in the objective with a penalty function. 

Surrogate optimization is for optimizing objective functions given by simulations, ODEs, PDEs, or other time-consuming computations. It attempts to find a global optimum while using few objective function evaluations.