%0 Journal Article
%T On Polynomial Optimization over Non-compact Semi-algebraic Sets
%A Vaithilingam Jeyakumar
%A Jean-Bernard Lasserre
%A G. Li
%J Mathematics
%D 2013
%I arXiv
%X We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems, the optimal value can be approximated as closely as desired by solving a hierarchy of semidefinite programs and the convergence is finite generically. Moreover, the Archimedean condition (as well as a sufficient coercivity condition) can also be checked numerically by solving a similar hierarchy of semidefinite programs. In other words, under reasonable assumptions the now standard hierarchy of SDP-relaxations extends to the non-compact case via a suitable modification.
%U http://arxiv.org/abs/1304.4552v2