Moment-Sum-of-Squares relaxations for variational problems

Next May 13, 2024 our Senior scientist Prof. Dr. Giovanni Fantuzzi will talk on “Moment-Sum-of-Squares relaxations for variational problems” organized within the research seminars “Nečas Seminar on Continuum Mechanics” at the Faculty of Mathematics and Physics of the Charles University (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.

Mon. May 13, 2024 at 15:40H

On-site / Online

[On-site] Room K3. Faculty of Mathematics and Physics. Charles University
Sokolovská 83 Prague 8

[Online] Live on YouTube: