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SUMMARY:Giovanni Fantuzzi (University of Erlangen)
DTSTART:20240513T134000Z
DTEND:20240513T151000Z
DTSTAMP:20260405T175425Z
UID:NSCM/132
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NSCM/132/">M
 oment-Sum-of-Squares relaxations for variational problems</a>\nby Giovanni
  Fantuzzi (University of Erlangen) as part of Nečas Seminar on Continuum 
 Mechanics\n\nLecture held in Room K3\,  Faculty of Mathematics and Physics
 \, Charles University\, Sokolovská 83  Prague 8..\n\nAbstract\nMoment-Sum
 -of-Squares (moment-SOS) relaxations are an established technique to compu
 te converging sequences of lower bounds on the global minimum of finite-di
 mensional polynomial optimization problems. In this talk\, I will discuss 
 two recent extensions of moment-SOS relaxations to infinite-dimensional va
 riational problems\, where a (possibly nonconvex) integral functional is t
 o be minimized over functions from a Sobolev space. The first extension op
 timizes so-called "null Lagrangian translations" and returns certified low
 er bounds on the global minimum of the variational problem. The second ext
 ension\, instead\, produces upper bounds by approximating minimizers of fi
 nite element discretizations of the variational problem. Conditions that e
 nsure the convergence of these upper and lower bounds to the desired globa
 l minimum will be discussed\, and current gaps between theory and practice
  will be illustrated by means of examples.\n
LOCATION:https://researchseminars.org/talk/NSCM/132/
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