Positivity and Optimization for Semi-Algebraic Functions

@article{Lasserre2010PositivityAO,
  title={Positivity and Optimization for Semi-Algebraic Functions},
  author={Jean Bernard Lasserre and Mihai Putinar},
  journal={SIAM J. Optim.},
  year={2010},
  volume={20},
  pages={3364-3383}
}
We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis on algebras generated by semi-algebraic functions. In this case the standard global optimization problem, with constraints given by elements of the same algebra, is reduced via a natural change of variables to the better-understood case of polynomial optimization. A collection of simple examples and numerical experiments complement the… 
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