Global Optimization of Polynomials Using the Truncated Tangency Variety and Sums of Squares

@article{Vui2008GlobalOO,
title={Global Optimization of Polynomials Using the Truncated Tangency Variety and Sums of Squares},
author={H{\`a} Huy Vui and Pham Tien So'n},
journal={SIAM Journal on Optimization},
year={2008},
volume={19},
pages={941-951}
}

This paper proposes a method for finding the global infimum of a multivariate polynomial f via sum of squares (SOS) relaxation over its truncated tangency variety. This variety is truncated of the set of all points x ∈ Rn where the level sets of f are tangent to the sphere in Rn centered in the origin and with radius ‖x‖. It is demonstrated that: • The infimum of f on Rn and on its truncated tangency variety coincide. • A sums of squares certificate for nonnegativity of f on its truncated… CONTINUE READING