# Positivity and Optimization for Semi-Algebraic Functions

@article{Lasserre2010PositivityAO,
title={Positivity and Optimization for Semi-Algebraic Functions},
author={Jean B. Lasserre and Mihai Putinar},
journal={SIAM J. Optim.},
year={2010},
volume={20},
pages={3364-3383}
}
• Published 27 October 2009
• Mathematics
• SIAM J. Optim.
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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