Indirect method by shooting

Summary

The indirect method by shooting solves an optimal control problem by first writing the necessary conditions of Pontryagin's maximum principle and then solving them numerically. These conditions form a two-point boundary value problem for the state and the costate. The unknown initial costate is found by the shooting method: one integrates forward from a guess and corrects the guess until the final conditions hold. The method is very accurate near a good guess, and it is the main alternative to direct methods such as direct collocation.