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Positive polynomials on projective limits of real algebraic varieties

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2009

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Putinar, Mihai

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http://nbn-resolving.de/urn:nbn:de:bsz:352-167433
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https://doi.org/10.1016/j.bulsci.2008.06.001
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Bulletin des Sciences Mathématiques. 2009, 133(1), pp. 92-111. ISSN 0007-4497. Available under: doi: 10.1016/j.bulsci.2008.06.001

Zusammenfassung

We reveal some important geometric aspects related to non-convex optimization of sparse polynomials. The main result, a Positivstellensatz on the fibre product of real algebraic affine varieties, is iterated to a comprehensive class of projective limits of such varieties. This framework includes as necessary ingredients recent works on the multivariate moment problem, disintegration and projective limits of probability measures and basic techniques of the theory of locally convex vector spaces. A variety of applications illustrate the versatility of this novel geometric approach to polynomial optimization.

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510 Mathematik

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ISO 690KUHLMANN, Salma, Mihai PUTINAR, 2009. Positive polynomials on projective limits of real algebraic varieties. In: Bulletin des Sciences Mathématiques. 2009, 133(1), pp. 92-111. ISSN 0007-4497. Available under: doi: 10.1016/j.bulsci.2008.06.001
BibTex
@article{Kuhlmann2009Posit-16743,
  year={2009},
  doi={10.1016/j.bulsci.2008.06.001},
  title={Positive polynomials on projective limits of real algebraic varieties},
  number={1},
  volume={133},
  issn={0007-4497},
  journal={Bulletin des Sciences Mathématiques},
  pages={92--111},
  author={Kuhlmann, Salma and Putinar, Mihai}
}
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