The relationship between the maximum principle and dynamic programming

@article{Clarke1987TheRB,
title={The relationship between the maximum principle and dynamic programming},
author={F. H. Clarke and R. Vinter},
journal={Siam Journal on Control and Optimization},
year={1987},
volume={25},
pages={1291-1311}
}

Let $V(t,x)$ be the infimum cost of an optimal control problem, viewed as a function of the initial time and state $(t,x)$. Dynamic Programming is concerned with the properties of $V( \cdot , \cdot )$ and in particular with its characterization as a solution to the Hamilton–Jacobi–Bellman equation. Heuristic arguments have long been advanced relating the Maximum Principle to Dynamic Programming according to \[p(t) = - V_x \left( {t,x_0 (t)} \right).\] Here $x_0 ( \cdot )$ is the minimizing… CONTINUE READING