Field optimization using the calculus of stationary points

The calculus of stationary points or indirect optimization is noted for rapid speed. It's speed is realized in an analytical representation of the Hessian and a polynomial fit of both the objective function and the constraints. Constraints are treated as active using Lagrangian multipliers. Because the algorithm's speed is so rapid, the problem can be repeated multiple times with random starting guesses to circumvent the possibility of encountering local wells. Both an analytic and an actual field problem are considered by way of providing examples of the technique.