Algebraic Degree in Semidefinite and Polynomial Optimization

  • Kristian Ranestad
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 166)


In polynomial optimization problems, where the objective function and the contraints are described by multivariate polynomials, an optimizer is algebraic. Its coordinates are roots of univariate polynomials whose coefficients are polynomials in the input data. The number of complex critical points estimates the degree of this polynomial, and is called the algebraic degree. We give some background, tools and examples on how to compute this degree in a number of different problem classes.


Complete Intersection Projective Variety Critical Locus Singular Locus Affine Space 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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