Corpus ID: 221949673

Stokes, Gibbs and volume computation of semi-algebraic sets

@article{Tacchi2020StokesGA,
  title={Stokes, Gibbs and volume computation of semi-algebraic sets},
  author={M. Tacchi and J. Lasserre and D. Henrion},
  journal={arXiv: Optimization and Control},
  year={2020}
}
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squares) methodology to a certain innite-dimensional linear program (LP). At each step one solves a semidenite relaxation of the LP which involves pseudo-moments up to a certain degree. Its dual computes a polynomial of same degree which approximates… Expand

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