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Algebraic Degree in Semidefinite and Polynomial Optimization

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Kristian Ranestad

    (University of Oslo)

Abstract

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.

Suggested Citation

  • Kristian Ranestad, 2012. "Algebraic Degree in Semidefinite and Polynomial Optimization," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 61-75, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_3
    DOI: 10.1007/978-1-4614-0769-0_3
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