Journal
MATHEMATICAL PROGRAMMING
Volume 96, Issue 2, Pages 293-320Publisher
SPRINGER-VERLAG
DOI: 10.1007/s10107-003-0387-5
Keywords
semidefinite programming; convex optimization; sums of squares; polynomial equations; real algebraic geometry
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A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible to a finite number of polynomial equalities and inequalities, it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility. The main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials, and some results from real algebraic geometry. The techniques provide a constructive approach for finding bounded degree solutions to the Positivstellensatz, and are illustrated with examples from diverse application fields.
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