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Certified Polynomial Optimization for System Verification

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 Victor Magron
Date
Le mardi 03 avril 2018 à 11:00
Lieu
Salle de Conférence (Pavillon des Jardins)
Orateur
Victor Magron (Verimag (Grenoble))

Semidefinite programming (SDP) is relevant to a wide range of mathematical fields, including combinatorial optimization, control theory, matrix completion. In 2001, Lasserre introduced a hierarchy of SDP relaxations for approximating polynomial infima. My talk emphasizes new applications of this SDP hierarchy in system verification, with a flavor of either computer science or mathematics, investigated during my research. In real algebraic geometry, I describe how to use these hierarchies to approximate as close as desired exact projections of semialgebraic sets. In nonlinear optimization, SDP hierarchies allow to compute Pareto curves (associated with multi-criteria problems) as well as solutions of transcendental problems. These hierarchies can also be easily interleaved with computer assisted proofs. An appealing motivation was to solve efficiently thousands of nonlinear inequalities occurring in the formal proof of Kepler Conjecture by Hales. Finally, SDP can provide precise information to analyze roundoff errors, motivated by automatic tuning of reconfigurable 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 dynamical systems, in particular reachable sets and invariant measures.


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mar. 19 février

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