Squared Functional Systems and Optimization Problems

  • Yurii Nesterov
Part of the Applied Optimization book series (APOP, volume 33)


In this paper we give an explicit description of the cones of polynomials represent able as a sum of squared functions. We prove that such cones can be always seen as a linear image of the cone of positive semidefinite matrices. As a consequence of the result, we get a description of the cones of univariate polynomials, which are non-negative on a ray and on an interval, and a description of non-negative trigonometric polynomials. We discuss some applications of the results to multi-variate polynomials.


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© Springer Science+Business Media Dordrecht 2000

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  • Yurii Nesterov

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