# Sandberg 200803

### From NA-Wiki

The development, evaluation, and application of the Symplectic Pontryagin method involves many members of the department. The method uses that minimizing functions to optimal control problems solve a Hamiltonian system when the Hamiltonian is differentiable. When it is not differentiable, a regularized Hamiltonian is used. I will describe the method, and a new convergence proof. It extends the previous result in the following ways:

1) Existence of solutions to Symplectic Pontryagin for a large class of problems.

2) The previous assumption on a bounded gradient of the dual variable with respect to state variables is no longer needed.

3) A slight improvement in the error bound.