Marco Mazzola

  Marco Mazzola - UPMC

• Main host organisation: Université Pierre et Marie Curie, Paris 6, France
  
• Supervisor: Hélène Frankowska
• Secondment organisation: Università di Roma La Sapienza in collaboration with Università di Roma Tor Vergata, Italy
• Nationality: Italian
• Fellowship duration: January 2011 - July 2012
• Email address

• Background: Marco obtained a PhD from the Università di Milano-Bicocca in 2010 on the following subject: "Properties of solutions to variational problems"

SADCO Project title: Relation of the adjoint state of the maximum principle to the value function

This research area concerns the relation between the value function and the adjoint arc featuring in the Pontryagin principle. It is known that, when the value function is differentiable, its gradient with respect to the state variable along an optimal trajectory coincides with the adjoint arc. For strictly convex problems we know, furthermore, that every optimal trajectory immediately penetrates the domain of differentiability of the value function. These properties provide insights into the structure of optimal solutions and establish a bridge between the variational methods, Pontryagin principle and the Hamilton-Jacobi equations. The aim here is to investigate analogous questions for state constrained problems. Advances in this areas can be expected to have an important consequences for the initialization of local solution methods, such as shooting methods. The latter are very accurate, but their radius of convergence is very small. Approximate calculation of the value might provide suitably accurate approximations to optimal arcs for initiation of shooting methods.

Publications