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Sums of squares and convex optimization


P.A. Parrilo

Linköping University, Sweden, Control and Communication Division

We present an overview of the convex optimization framework for semialgebraic problems recently introduced by the speaker. Along the way, we'll learn how to compute sum of squares decompositions for polynomials using semidefinite programming. The developed techniques, based on results from real algebraic geometry, unify and generalize many well-known existing methods, such as the S-procedure. The ideas and algorithms will be illustrated with examples from a broad range of domains, emphasizing the applications in systems and control theory, and the use of the SOSTOOLS software (developed in collaboration with Stephen Prajna and Antonis Papachristodoulou).

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