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Sum of squares optimization techniques for real algebra


P.A. Parrilo

Buenos Aires, Argentina, I Latin American Workshop on Polynomial Systems.

We present an overview of a convex optimization framework for semialgebraic problems. Along the way, we'll learn how to compute sum of squares decompositions for polynomials using semidefinite programming, and how to obtain infeasibility certificates for real solutions of polynomial equations. The developed techniques, based on results from real algebraic geometry, unify and generalize many well-known existing methods. The ideas and algorithms will be illustrated with examples from a broad range of domains, and the use of the SOSTOOLS software (developed in collaboration with Stephen Prajna, Antonis Papachristodoulou, and Pete Seiler).

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