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DTSTART:19700329T020000
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DTSTART:19701025T030000
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SUMMARY:
Certified Polynomial Optimization for System Verification
STATUS:CONFIRMED
ATTENDEE;CN="Victor Magron
":
MAILTO:no@spam.com
DESCRIPTION:
Semidefinite programming (SDP) is relevant to a wide range o
f mathematical fields\, including combinatorial optimization
\, control theory\, matrix completion. In 2001\, Lasserre in
troduced a hierarchy of SDP relaxations for approximating po
lynomial infima. My talk emphasizes new applications of this
SDP hierarchy in system verification\, with a flavor of eit
her computer science or mathematics\, investigated during my
research. In real algebraic geometry\, I describe how to us
e these hierarchies to approximate as close as desired exact
projections of semialgebraic sets. In nonlinear optimizatio
n\, SDP hierarchies allow to compute Pareto curves (associat
ed with multi-criteria problems) as well as solutions of tra
nscendental problems. These hierarchies can also be easily i
nterleaved with computer assisted proofs. An appealing motiv
ation was to solve efficiently thousands of nonlinear inequa
lities occurring in the formal proof of Kepler Conjecture by
Hales. Finally\, SDP can provide precise information to ana
lyze roundoff errors\, motivated by automatic tuning of reco
nfigurable hardware (e.g. FPGA) to algorithm specifications.
I will eventually focus on explaining how these hierarchies
allow to characterize sets of interest in control and dynam
ical systems\, in particular reachable sets and invariant me
asures.
DTSTART;TZID=Europe/Paris:20180403T110000
DURATION:PT1H
URL;VALUE=URI:http://www.lsv.ens-cachan.fr/Seminaires/?sem=201804031
100
UID:LSVsemLSV.201804031100@lsv.ens-cachan.fr
LOCATION:Salle de ConfĂ©rence (Pavillon des Jardins)
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