Publikation:

Optimization of polynomials on compact semialgebraic sets

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2005

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http://nbn-resolving.de/urn:nbn:de:bsz:352-156477
DOI (zitierfähiger Link)
https://doi.org/10.1137/S1052623403431779
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Published

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SIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779

Zusammenfassung

We give a short introduction to Lasserre's method for minimizing a polynomial on a compact basic closed semialgebraic set. It consists of successively solving tighter and tighter convex relaxations of this problem which can be formulated as semidefinite programs. We give a new short proof for the convergence of the optimal values of these relaxations to the minimum which is constructive and elementary. In the case that there is a unique minimizer, we prove that every sequence of nearly optimal solutions of the successive relaxations gives rise to a sequence of points converging to this minimizer.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

nonconvex optimization, positive polynomial, sum of squares, moment problem, Positivstellensatz, semidefinite programming.

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ISO 690SCHWEIGHOFER, Markus, 2005. Optimization of polynomials on compact semialgebraic sets. In: SIAM Journal on Optimization. 2005, 15(3), pp. 805-825. ISSN 1052-6234. Available under: doi: 10.1137/S1052623403431779
BibTex
@article{Schweighofer2005Optim-15647,
  year={2005},
  doi={10.1137/S1052623403431779},
  title={Optimization of polynomials on compact semialgebraic sets},
  number={3},
  volume={15},
  issn={1052-6234},
  journal={SIAM Journal on Optimization},
  pages={805--825},
  author={Schweighofer, Markus}
}
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