Accept our invitation to the seminar organized by the AIC research group with the support of the RCI project. Rodolfo Ríos Zertuche from French National Centre for Scientific Research (CNRS) and Artificial and Natural Intelligence Toulouse Institute (ANITI) will visit the department on March 23, 2023 to give a lecture about his recent work. Meet us in the room KN:E-301 at 14:30.
This seminar is funded by the RCI project.
After completing his master in CIMAT (Mexico), Rodolfo Ríos Zertuche did his PhD at Princeton, and has since been at ICERM - Brown University, the Max Planck Institute for Mathematics in Bonn, the Ecole Normale Superieure de Paris, the Artificial and Natural Intelligence Toulouse Institute, and the Laboratory for the Analysis and Architecture of Systems of CNRS. He has worked on various subjects that include representation theory, the calculus of variations, and optimization algorithms.
Solving PDE, variational, and optimal control problems using semidefinite programs via occupation measure relaxations
We will first review a few algorithms that have been proposed to solve (highly nonconvex) problems in PDEs, the calculus of variations, and optimal control, using hierarchies of tractable SDPs. These algorithms require the reformulation of the problem in a relaxed form that leverages a weaker concept of solution to expand the search to a set of measures that contains the space of functions. We will give geometric intuitions into how this works. The success of those schemes at solving the relaxed versions of the problems leaves open the question of whether they coincide with their classic counterparts. This is the question that we address in this work. The answer consists of statements that show the existence or absence of gaps, depending on the dimensions of the domain and the codomain of the solutions. We also describe examples in which the measure-valued solution appears to be more reasonable than the classical one.