# 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

#### References

SHOWING 1-10 OF 34 REFERENCES

Exploiting Sparsity for Semi-Algebraic Set Volume Computation *

- Mathematics, Computer Science
- 2019

Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets

- Mathematics, Computer Science
- Optim. Lett.
- 2018

Computing approximations and generalized solutions using moments and positive polynomials

- Computer Science
- 2018

Approximate Volume and Integration for Basic Semialgebraic Sets

- Mathematics, Computer Science
- SIAM Rev.
- 2009

Convex computation of the region of attraction of polynomial control systems?

- Mathematics, Computer Science
- 2013 European Control Conference (ECC)
- 2013

Computing Gaussian & exponential measures of semi-algebraic sets

- Mathematics, Computer Science
- Adv. Appl. Math.
- 2017

Computing the Hausdorff Boundary Measure of Semialgebraic Sets

- Computer Science, Mathematics
- SIAM J. Appl. Algebra Geom.
- 2020

Approximating regions of attraction of a sparse polynomial differential system

- Engineering, Computer Science
- ArXiv
- 2019