Positivity and Optimization for Semi-Algebraic Functions

Authors:
Jean B. Lasserre;Mihai Putinar
Affiliations:
lasserre@laas.fr;mputinar@math.ucsb.edu
Venue:
SIAM Journal on Optimization
Year:
2010

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Abstract

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 theoretical parts of the article.