Optimization of polynomials on compact semialgebraic sets

Schweighofer, Markus

Optimization of polynomials on compact semialgebraic sets

Files

convergence.pdf(1.56 MB)

Date

2005

Publication type

Journal article

Published in

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.

Subject (DDC)

510 Mathematics

Keywords

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

Cite This

ISO 690

SCHWEIGHOFER, 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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