Within the ROBOPROX Project, we would like to invite you to the lecture by Prof. Giovanni Fantuzzi who will be in Prague on 13 May 2024:
“Moment-Sum-of-Squares relaxations for variational problems”
Prof. Fantuzzi is an expert in optimization, dynamical systems, fluid
mechanics, and partial differential equations.
Join us on 13 May 2024 at 15:40 at the Faculty of Mathematics and Physics of the Charles University (MFF UK) in Prague 8 – Karlín and learn about the latest developments in this area.
The event is organised within the research seminars “Nečas Seminar on Continuum Mechanics” of MFF UK.
Abstract: Moment-Sum-of-Squares (moment-SOS) relaxations are an established technique to compute converging sequences of lower bounds on the global minimum of finite-dimensional polynomial optimization problems. In this talk, I will discuss two recent extensions of moment-SOS relaxations to infinite-dimensional variational problems, where a (possibly nonconvex) integral functional is to be minimized over functions from a Sobolev space. The first extension optimizes so-called “null Lagrangian translations” and returns certified lower bounds on the global minimum of the variational problem. The second extension, instead, produces upper bounds by approximating minimizers of finite element discretizations of the variational problem. Conditions that ensure the convergence of these upper and lower bounds to the desired global minimum will be discussed, and current gaps between theory and practice will be illustrated by means of examples.
