Positivity and optimization for semi-algebraic functions

Details Positivity and optimization for semi-algebraic functions Positivity and optimization for semi-algebraic functions

2009-10-27

arxiv.org/abs/0910.5250v2

Mathematics

Optimization and Control

20 pages

Scientific paper

We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which 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 theoretical parts of the article.

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