Optimization of polynomials on compact semialgebraic sets

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2005
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SIAM Journal on Optimization ; 15 (2005), 3. - pp. 805-825. - ISSN 1052-6234
Abstract
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.
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510 Mathematics
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nonconvex optimization,positive polynomial,sum of squares,moment problem,Positivstellensatz,semidefinite programming.
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Cite This
ISO 690SCHWEIGHOFER, Markus, 2005. Optimization of polynomials on compact semialgebraic sets. In: SIAM Journal on Optimization. 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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