Algebraic Degree in Semidefinite and Polynomial Optimization

Kristian Ranestad ()
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Kristian Ranestad: University of Oslo

Chapter Chapter 3 in Handbook on Semidefinite, Conic and Polynomial Optimization, 2012, pp 61-75 from Springer

Abstract: 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.

Keywords: Complete Intersection; Projective Variety; Critical Locus; Singular Locus; Affine Space (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0769-0_3

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