Pontryagin's Minimum Principle - Maximization and Minimization

Maximization and Minimization

The principle was first known as Pontryagin's maximum principle and its proof is historically based on maximizing the Hamiltonian. The initial application of this principle was to the maximization of the terminal velocity of a rocket. However as it was subsequently mostly used for minimization of a performance index it has here been referred to as the minimum principle. Pontryagin's book solved the problem of minimizing a performance index.