On the existence of the solution to the Hamilton-Jacobi equation by using the dual dynamical programming

الملخص EN

Properties of the value function and dual value function for an optimal control problems of Lagrange and Bolza are described.

A main theorem is proved, this theorem deals with the existence of a maximum solution to the Hamilton - Jacobi equation for the Lagrange problem, with satisfies the Lipschitz condition by using the dual dynamic programming method.

Finally gives an example which illustrates the value of the main theorem.